Application of derivatives Questions and Answers

Minimize f x y x y2 subject to 8x 4y 80 X y 0 The value of f at the minimum is

se backward difference formula to evaluate the first derivative of y tan x at x using a value of h 12 05 2 1 O4 3 3 M 06 2 3 O 0 2 1

A a daki lineer sistem i in Gauss Seidel y nteminin T matrisinin spectral yar ap n bulunuz Find the spectral radius of the matrix T of Gauss Seidel method for the following lineer system X 2x x3 2 X X 2xy 3 2x 2x x 2 02

UT 2TT 3 Given log54 x and log53 y determine an expression for logs whole numbers 5 marks 2TT 4 T 27 2000 in terms of x y and

4 Solve the followin a 4x 7x 3

x 34 y 81 x 1 1093 5 X 0 6 Given f x x 4 g x 4x 7 h x 2x 4 3 determine the following where possi a fog x 2 2 2 marks b f g 1 c goh 4

5 A person wants to invest 20 000 for 2 years and is considering two different investments The first investment a money market fund pays a guaranteed 5 8 interest compounded daily The second investment a treasury note pays 5 9 annual interest Which investment pays the mo interest over the 2 year period Select the correct choice below and if necessary fill in any answer box es to complete your choice Do not round until the final answer Then round to the nearest cent as needed OA The treasury note is the better investment since the market fund produces in interest and the treasury note pays OB The market fund is the better investment since the market fund produces in interest and the treasury note pays OC Both the market fund and the treasury note produce the same interest with in interest in interest

Click to enlarge graph d Find the domain and the range of the quadratic function The domain of fis Type your answer in interval notation The range of fis Type your answer in interval notation e Determine where the quadratic function is increasing and where it is decreasing The function is increasing on the interval Type your answer in interval notation The function is decreasing on the interval Type your answer in interval notation f Determine where f x 0 and where f x 0 Select the correct choice below and fill in the answer box es within your choice Type your answer in interval notation Use integers or fractions for any numbers in the expression OA f x 0 on OB f x 0 on O C f x 0 on and f x is never positive and f x 0 on and f x is never negative

The following money market account rates were available from a particular bank Find the compound amount and the interest earned 16 000 at 0 91 compounded monthly for three years The compound amount is Do not round until the final answer Then round to the nearest cent as needed The interest earned is Do not round until the final answer Then round to the nearest cent as needed

On the graph below move the two points to graph the slant asymptote for the function f x Provide your answer below 10 51 10 4x 6x 2x 1

Find 2 2 1 x 4 X 4 y 4 z 4 lim P 5 2 2 14 7 4 2 1 0 Z 4 lim P 5 2 2 X 4 Type an integer or a simplified fraction

Verify that wxy Wyx for w In 8x 5y

Identify the rational function whose graph is given below Note that the function has an x intercept at x 3 and a y 3 The graph has one vertical asymptote at x 2 intercept of y 2 15 10 10 15 N Im 6 S LO

Find the slope of the line graphed below

by setting the x intercept and the moving asymptotes Provide your answer below 10 3 0 10 5 0 0 0 5 3 0 5 x 2 10

by setting the moving points correctly Provide your answer below 10 3 5 0 5 10 5 0 0 0 5 2 0 f x x 2 x 1 x 3 5 0 10

Find the slope of the line graphed below N

Graph the function below by moving the vertical asymptotes and the x intercept to the correct end behavior of the function is correct Provide your answer below End Behavior 10 10 f x 5 X 2 x 4 x 1 10

by setting the moving points correctly Sorry that s incorrect Try again 10 5 10 5 0 5 2 0 f x 11 5 0 x 2 10

A highway and a railway cross at and angle of 32 degrees A freight train is approaching the intersection at 64 miles per hour while a car is approaching the intersection at 11 miles per hour Determine the rate of change of the distance between the freight train and the car when the freight train and the car are 1 and 5 miles away from the intersection respectively Round the solution to the nearest ten thousandth if necessary miles per hour car freight train

A highway and a railway cross at and angle of 22 degrees A passenger train is approaching the intersection at 74 miles per hour while a car is approaching the intersection at 80 miles per hour Determine the rate of change of the distance between the passenger train and the car when the passenger train and the car are 5 and 1 miles away from the intersection respectively Round the solution to the nearest ten thousandth if necessary miles per hour car passenger train

Consider the parabola y 6x x a Find the slope of the tangent line to the parabola at the point 1 5 b Find an equation of the tangent line in part a y c Graph the parabola and the tangent line y 20 10 20 10 10 20 10 20 20 DO 10 y 20 10 10 201 10 20 X 20 O 10 y 20 10 10 20F 10 20 20 O 10 y 20 10 10 20

11 G 9 Q Find the area of the shaded region Round your answer to the nearest tenth Question Help OVideo Message Instructo Calculator

Let A z f t dt with fix shown in the graph below 2 1 3 2 4 At what x values does A x have a local max x At what x values does A x have a local min x Restrict your answers to values 0 x 6 Question Help Video Message instructor N 2

Find the area of the parallelogram shown below 10 9 Q 8 K 6 I m TH 1 2 3 4 5 6 7 8 9 10 1 Area Question Help Video Message instructor Calculator

A disease spreads through a population The number of cases t days after the start of the epidemic is shown below Days after start t Number infected N t thousand 56 64 6 12 Assume the disease spreads at an exponential rate How many cases will there be on day 77 to the nearest thousand o On approximately what day will the number infected equal ninety thousand of Round your answer to the nearest whole number thousand Round your answer

Find the area of the figure pictured below 8 6 yd Area 4 4 yd 10 8 yd 3 5 yd Q yd Question Help Worked Example 1 Message instruc

There are currently o threads in this forum Create a thread to help start the conversation Create Thread FORUM DESCRIPTION Topic for initial post Write or type an exemplar for a homework question from this module An exemplar is an example of perfect work Choose one homework exercise and create a detailed perfect solution You may type your exemplar or post a photo Be sure to include the original question along with the solution Peer Response Critique the work of one of your fellow students whose work has not previously been critiqued this will allow each student to receive feedback Check their solution Is it Correct Kindly help identify any errors in the post you choose to critique

The rate of change of the bacteria is proportional to the population at a given time Let B t be the number of bacteria in the population where t is measured in years Use differential equations to find the general solution to for B t where B 0 is the initial population 100 and r is the rate of growth

The graph of y f x is shown in the figure above On which of the following intervals are 20 0 and 0 I a x b II b x c III c x d OA I only OB II only C III only OD I and II y f x E II and III

Use the graph to find f 0 f 0 MI

Let f be a function that is continuous on the closed interval 2 3 such that f 0 does not exist f 2 0 and f x 0 for all x except x 0 Which of the following could be the graph of f A C h in t t OA OB Oc OD B D E

2 f x 2 x Stepi Slope of tangent line lim X 9 f x f 9 x 9 Step 2 plug into equation Check f x 2 9 function of 9 6 A Step 3 f x lim f a h f a Solve nyo 12 n distance 3 X f 9 h f 9 n

A line segment joins the points 8 5i and 2 9i on the complex plane What are the length and the midpoint of the segment O2 29 5 2i 2 29 6 14 2 58 5 2i 2 58 6 14i

4 A 7 2 7 A N 1 2 3 Y 1 2 3 4 Real axis 5 her that point A represents

The domain of r 4sin 38 is restricted to produce the graph shown 2 3T 2

Write an inequality and solve it to answer the question Do not round the answer The final grade in an algebra course is based on a weighted average homework counts 30 tests count 45 and the final exam counts 25 A student has a homework average of 85 5 and a test average of 79 What score does the student need on the final exam to get at least an 80 for the final course grade A or higher on the final exam

2 f x 2 x Stepi Slope of tangent line lim Xx 9 f x f 9 X X 9 Step 2 plug into equation Check f x 2 9 function of 9 6 A n distance B X 6 Step 3 f x lim f a r f a f 9th f 9 Solve no h

Meghan is a psychology major who is testing a maze for a group of mice to navigate In order for it to be productive for a class project she would like the average time for a mouse to complete the maze to be 90 seconds She randomly selects 28 mice and has each mouse complete the maze Meghan records the time in seconds that each mouse needed to complete the maze The results are provided in the accompanying data table Based on research and previous results Meghan assumes that the population is normally distributed and the population standard deviation is 5 80 seconds Use Excel to test whether the mean amount of time a mouse completes the maze is 90 seconds and then draw a conclusion in the context of the problem where a 0 10 Select the correct answer below Help Time seconds 85 71 93 16 87 00 89 71 94 26 92 05 86 16 82 16 94 76 Copy to Clipboard Download CSV Fail to reject the null hypothesis There is sufficient evidence at the a 0 10 level of significance to conclude that the mean amount of time a mouse completes the maze is greater than 90 seconds Fail to reject the null hypothesis There is insufficient evidence at the a 0 10 level of significance to conclude that the mean amount of time a mouse completes the maze is not equal to 90 seconds

Consider the following graph on the interval 270 x 105 270 240 210 180 150 120 90 60 30 1 What is the amplitude of the function 2 What is the period of the function 360 3 What is the equation if the function y 3 30 60 90

Let f x mx 17 if x 10 x 9x 7 if x 10 If f x is a function which is continuous everywhere then we must have m A

Find the column matrix of constants 5a 3b c 1 6a 3b c 6 4a 2b c 5 O 6 5 F 6 5 CT LO

Find the direction cosines and direction angles of the vector Give the direction angles correct to the nearest tenth of a degree 21 j 6k cos a cos p cos y B Y 11

4 find lim g x X 1 where f x x 3x 2 4 if x 1 if x 1

If the function f is defined by f x x 1 then the inverse f 1 is defined b f x O x 1 Ox 1 O 1 x 1 O x 1 3 H

A construction worker pulls a five meter plank up the side of a building under construction by means of a rope tied to one end of the plank see figure Assume the opposite end of the plank follows a path perpendicular to the wall of the buildin and the worker pulls the rope at a rate of 0 12 meter per second How fast is the end of the plank sliding along the groun when it is 1 9 meters from the wall of the building Round your answer to two decimal places m sec 5 m

he graph from the US Department of Energy shows how driving speed affects gas mileage Fuel economy F is measured in miles per gallon and speed v is measured in miles per hour F mi gal 30 y 20 10 1 0 10 20 30 40 50 60 a What is the meaning of the derivative F v O F v is the instantaneous rate of change of speed with respect to fuel economy O F v is the instantaneous rate of change of distance with respect to speed b Sketch the graph of y F v 70 mi h O F v is the instantaneous rate of change of fuel economy with respect to speed OF v is the instantaneous rate of change of speed with respect to distance O F v is the instantaneous rate of change of fuel economy with respect to distance 10 20 10 20 30 40 50 60 70 pergales V V 70 10 70 V 10 20 30 40 50 60 G 20 30 40 50 60 30

Find the open intervals on which the function is increasing or decreasing h x 5 xe x increasing decreasing

A spinner marked off in eight equal sized regions numbered 1 2 3 4 5 6 7 and 8 is spun once Let the random variable X be the number of the region where the pointer stops and define a probability mass function f x P X x a State the range of X b Write f as a set of ordered pairs c Draw the probability distribution as a histogram d Find f 3 and explain what this number represents e Find and explain what this number represents OA Ay 12345678 Q A The value of f 3 is B 8 OA The mean is OB The mean u is 12 1 2 3 4 5 6 7 8 78 d Select the correct choice below and if necessary fill in the answer box to complete your choice Type an exact answer in simplified form Use the answer from part b to find this answer Q 1 and represents the probability the spinner lands on that region 8 B The value of f 3 is and represents the average value of the spins e Select the correct choice below and if necessary fill in the answer box to complete your choice and represents the average value of the spins and represents the probability of landing on one of the regions CIB C 1 9 0123456 SOU OD co 01234567 4 SOU

Let h x ex Determine the equation of the tangent line to h at x 1 Report the solution using slope intercept form Suchmit O