Application of derivatives Questions and Answers

The power delivered by a battery to an apparatus of resistance R in ohms is P R power with respect to resistance for R 69 Use decimal notation Give your answer to four decimal places The rate of change is approximately 2 4R W Find the rate of change of R 0 5 W S

Use the information about values of the functions and their derivatives to calculate G 2 where G x x g x f x f 2 8 f 2 11 g 2 13 Use symbolic notation and fractions where needed g 2 2

Calculate the first second and third derivatives of y x x54x Use symbolic notation and fractions where needed y x y x

Find the rate of change for the area of a square with respect to its side s when s 14 Give your answer as a whole or exact number The rate of change is square units per unit incre

Find the exact location of all the relative and absolute extrema of the function Order your answers from smallest to largest x f x x48x3 with domain 1 The variable has an absolute maximumx at x y The variable has a relative minimum xat x y 1 9 6 432

Identify the horizontal and vertical asymptotes if any of the given function f x Separate multiple answers by commas Enter DNE if an asymptote does not exist a Horizontal asymptote s y 8 3 b Vertical asymptote s DNE help numbers 8x 32x 24 3x212x15

6 Given that sin and the angle is in the first quadrant find the value for cos 0 91 O 100 O 91 10 O 900 100 91

A group of 457 individuals was surveyed They were asked whether they were asked their gender and whether they drove a car a truck or an SUV The results are sumarized in the contingency table below car truck suv total male 75 77 79 231 female 87 17 122 226 total 162 94 201 457 a What percentage of those surveyed were female and drove a car Round your answer to one decimal place b What percentage of the men drove a truck Round your answer to one decimal place c What percentage of suv drivers were women Round your answer to one decimal place

For the given points P Q and R find the approximate measurements of the angles of APQR P 0 1 5 Q 2 2 1 R 4 4 3 The measure of ZP is Pound to the nearest tonth as pooded

data given below answer parts a 6 7 8 4 5

In parts a f use the given figure a Solve f x 18 b Solve f x 36 c Solve f x 0 d Solve f x 18 e Solve f x 36 f Solve 0 f x 36 a For what value of x does f x 18 7 Ay y f x 36 36 12 18 12 0 X Q Q

Find A the area of the region under the curve y 2 2x2 and above the x axis B

S Solve the equation 16 2t 2 Select the correct choice below QA There is one solution t

For the data listed below which value is the mode 200 219 234 234 236 238 240 243 245 245 245 247 247 248 249 251 252 O 252 O 200 O243 245

Use the given graph of y f x to find the intervals on which f x 0 the intervals on which f x 0 and the values of x for which f x 0 Sketch a possible graph of y f x G On what subinterval s is f x 0 Select the correct choice below and if necessary fill in the answer box to complete your ch OA Type your answer using interval notation Use a comma to separate answers as needed OB There are no such subintervals

The height of a plant over time is shown in the table below Using a logarithmic model what is the best estimate for the age of the plant when it is 19 inches tall 10 months 14 months 16 months 28 months t time in months 1 2 3 4 5 6 Plant Height h height in inches 18 18 21 18 33 18 42 18 48 18 54

For each of the following tables use the given information to fill in the missing entry then define the function formu for each relationship Assume that each relationship is an exponential function a Complete the table of values below The function formula is f x b Complete the table of values below The function formula is 4 x 1 5 0 1 2 3 7 25 Preview x 0 1 2 4 6 5 6 Preview y f x 27 8346 38 9 48 625 60 7813 196 1314 y g x 18 18 72 21 5589 22 4212

Devon purchased a new car valued at 16 000 that depreciated continuously at a rate of 35 Its current value is 2 000 The equation 2 000 16 000 1 r represents the situation where t is the age of the car in years and r is th rate of depreciation About how old is Devon s car Use a calculator and round your answer to the nearest whole number O 1 year 2 years O 5 years 8 years

1 How does the value of log2 100 compare with the value of log 20 The value of log2100 is about 4 times the value of log 20 O The value of log2 100 is about a times the value of log 20 The value of log2100 is about 3 times the value of logs 20 The value of log2 100 is about 3 times the value of log 20

A population of insects increases at a rate of 1 5 per day About how long will it take the population to double O 2 5 days O 5 0 days 46 6 days 66 7 days

If the equation below is solved by graphing which statement is true log 6x 10 log 1 X 2 The curves intersect at approximately x 0 46 The curves intersect at approximately x 0 75 O The curves intersect at approximately x 1 11 The curves intersect at approximately x 3 07

For what value of n does O 3 0 13 1 02 0 2 03 36 n 2162

Which of the following is true about the base b of a logarithmic function O b 0 and b 1 O b 0 and b 1 Ob 0 and b 1 Ob 0 and b 1

What is the value of log62557 0 4 O T 1 qadin 4

Find the slope of the tangent line to the sine function at the origin a b y 2 1 2 y 2 KIN RF 2 y sin x K 3A 2 2A y sin 8 x MMMM X 2A X i

Lightning travels much faster t seen before thunder is heard and the graph to the right if you lightning and thunder how far mi away

K The circumfer The circle s r

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8 0 52 Points DETAILS LARCALC12 2 2 005 Use the graph to estimate the slope of the tangent line to y 1 2

b y x 1 1 y 4 3 2 H 1 2 1 1 1 2

The height of a ball t seconds after it is thrown from the top of a building is given by H t 16t 67t 124 Find its height velocity and acceleration 5 seconds after it is thrown from the building The ball s height after 5 seconds is The ball s velocity after 5 seconds is ft The ball s acceleration after 5 seconds is ft sec ft sec 2

14 For each of the problems below rewrite it as a missing factor multiplication question Then find the quotient using what you know about multiplying fractions a 9 10 3 5 b 7 8 1 4 c 6 7 3 7 d 10 9 2 3 e 25 12 5 6

Question 5 Part 1 of Use inductive reasoning to predict th equence of computations Then us erform the arithmetic by hand to de onjecture is correct

and Proof K Use inductive reaso sequence of comput perform the arithmet conjecture is correct

he graph of one complete period of a sine curve is given y 1 2 period 8 horizontal shift 22 a Find the amplitude period and horizontal shift Assume the absolute value of the horizontal shift is le the period amplitude WebAssign Plot b Write an equation that represents the curve in the form y a sin k x b

X X Let f t 2t 14 and consider the two area functions A x f t dt and F x f t dt Complete parts a c 1 dl and Fix S 10 Use geometry to find an expression for A x when x 27 x 14x 49 Type an expression using x as the variable b Evaluate F 11 and F 12 Then use geometry to find an expression for F x for all x2 10 The value of F 11 is 7 Simplify your answer The value of F 12 is 16 Simplify your answer Use geometry to find an expression for F x when x 2 10 14x 40 Type an expression using x as the variable c Show that A x F x is a constant and that A x F x f x First prove A x F x is a constant Given A x x 14x 49 and F x x 14x 40 subtract F x from A x The value of A x F x is 9 Simplify your answer Now prove that A x F x f x Given A x and F x take the derivative of A x and F x respectively and compare the results A x x 14x 49 Simplify your answer Do not factor

marginal cost when Q 8 if a total cost function is given by TC 1 3 Q 3 30Q 2 2800Q 2800

The functions fand g are defined as follows 2 f x 4x 3 g x 5x 1 Find f 3 and g 7 Simplify your answers as much as possible f 0 8 7 0 g X

3 5 ne missing coordinates of the points that lie on the of y x and the corresponding points that lie on the of f x x 3 5 ts that lie on the raph of y x 1 f x x 3 5 lify your answers Type ordered pairs Simplify your answer 0 1 Corresponding points that lie on the graph of main of f x is your answer in interval notation

A bucket filled with sand has a total mass of 25 kg Your friend begins steadily lifting the bucket to the top of a building 10 meters above the ground using a cable of negligible mass but the bucket has a hole in it and leaks 0 2 kg of sand for each meter your friend lifts it The work your friend does lifting the bucket to the top of the building is Recall that acceleration Joules to gravity 9 81

Starting with the graph of a basic function following function using the techniques of s compressing stretching and or reflecting and range of the function g x x 6 Use the graphing tool to graph the equatic

Find the measure of the side of the right triangle whose length is designated by a lowercase letter b Round answers to the nearest whole number A 145 in 51 b be in Do not round until the final answer Then round to the nearest whole number B C

Find the real solutions of the equ

a Use a graphing utility to graph f x x minima b Determine where f is increasing and whe

a Use a graphing utility to graph f x 2 minima

luate 15C nplify your answer Type an integer or a fraction

Question 26 8 4 17 Part 3 of 4 et P Z 0 42 P Y 0 40 and P ZnY 0 19 Use a Wenn diagram to find a P Z nY b P Z UY c ZUY and d P ZnY a P Z nY 0 37 Type an integer or a decimal Type an integer or a decimal D P ZUY 0 81 c P Z UY 0 87 Type an integer or a decimal EXK accom

5 Given integral 2 dx dy y dx dy do the following 30 points 10 each a Sketch the region of integration b Rewrite the integrals by reversing the order of integration

The table shows the numbers y of bacteria that grow on a sandwich x hours after it is left in the sun Hours x 1 2 3 4 Number of Bacteria y 25 75 225 675 Write a function that models the data

Class Work 2 CPSC 3271 Introduction to Numerical Solutions Name Please show all your work no work no credit 1 Employ Fixed Point Iteration Method to locate the root of f x 0 5e X X Use an initial guess of Xo 0 and iterate until EO 1 Verify that the process is linearly convergent with checking if g x 1 Fixed Point Iteration Method g x f x x 2i 1 g 2i x five iterations Approximate absolute percent relative error is X 1 Jai