Application of derivatives Questions and Answers

Multiply in the indicated base 33 six x 5 six The product is six

Multiply in the indicated base 245 x 35 245 x 35 3 4 0 X01 2 000 0 101 2 202 4 11 1 30 3 11 14 2 40 4 13 22 3 2

Subtract the given numbers in the indicated base 32 five 24 five he difference is five

Compute y for y 3x 1 x 6 03 y 27 3x 1 x4 6 4x 3x 1 x 6 y 27 3x 1 x4 6 13x 4x 54 y 3 3x 1 x4 6 2 21x 4x 54 y 27 3x 1 x4 6 9x 3x 1 x 6 y 27 3x 1 x 6 x 3x 1 x 6

Listen Determine f x for f x 1 6x 0 f 2 b 3 1 6x O 0 f1 z or 3 1 6x 3 fi 2 6 0 f 2 1 te 3 1 6x

Listen If an equation of the tangent line to the curve y f x at the point where a 3 is y 4x 9 determine f 3 and f 3 none of these f 3 3 f 3 3 f 3 3 f 3 3 f 3 3 f 3 4 f 3 9 f 3 4

Determine the equations of the tangent lines to the curve y parallel to the line x y 8 Ox y 17 x y 1 x y 4 x y 1 Ox y 17 x y 1 x y 17 x y 1 x y 17 x 8 x 8 that are

sin x Differentiate y 3 cos x Ody dx Ody dx Ody dx Ody dx Ody da 3 cos x 1 3 cos x 4 3 cos x 4 3 cos x 3 cos x 1 3 cos x 1 3 cos x

Listen Differentiate g x 9sec x tan x Og x 9 tan x sec x None of these g x 9sec x tan x sec x Og x sec x tan x sec x Og x 9sec x tan x sec x

The population of a city can be modeled by P t 39e0 05 thousand persons where t is the number of years after 2000 Approximately how rapidly was the city s population be changing between 2023 and 2032 The city s population was changing by answer rounded to at least three decimal places thousand persons year Enter your

4 2 12 10 8 6 4 2 2 4 6 8 10 12 Dot Line Segment a Mark the two points on the graph that are needed to calculate Average Rate of Change over the interval 1 3 b Connect the points with a line segment c The Average Rate of Change over 1 3 is 8 10 x 4

Find the distance between the pair of points 1 5 and 2 8 The distance is Round to the nearest thousandth as needed

The population of a city can be modeled by P t 36e0 05t thousand persons where t is the number of years after 2000 Approximately how rapidly was the city s population be changing between 2026 and 2035 The city s population was changing by Speyer rounded to at least three decimal places thousand persons year Enter your

The graph of P t below shows the population in thousands of people of a city t years after 2008 Note that 8 years after 2008 the population is approximately 5 55 thousand people And 16 years after 2008 the population is approximately 10 28 thousand people Approximate the average rates of change over each of the following time intervals Round to two decimal places 0 years to 8 years Select an answer 8 years to 16 years Select an answer 0 years to 16 years Select an answer V Population in Thousands 114 10 94 8 2 1 15 6 17 8 9 10 11 12 13 14 15 16 Years since 2008 Complete the statement to explain the meaning of the rate of change in this situation The city s population is Select an answer at Select an answer What do the values above tell you about the rate of change of V t rate

1 5 5 5 4 5 4 3 5 3 2 5 2 0 5 0 5 0 5 0 5 I 1 5 2 2 5 3 3 5 4 O 1 Based on the graph above select the statement that is true O The average rate of change from x 0 to x 1 is more than the average rate of change from x 2 to x 3 O The average rate of change from x 0 to x 1 is less than the average rate of change from x 2 to x 3 O The average rate of change from x 0 to x 1 is equal to the average rate of change from x 2 to x 3

Given the points 10 10 and 9 1 find the rate of change between the points Answer Round to three 3 decimal places

Given the tables for f g below find the following f x g x 2 6 7 9 3 8 0 1 4 5 1 NOT 2 4 6 8 CN 9 2 3 6 95 N 1 Average rate of change of g from 1 to 4

nvert the numeral to a numeral in base ten FFF4 sixteen

Convert the numeral to a numeral in base ten 11 6368

Convert the numeral to a numeral in base ten 1100012 The numeral in base 10 is 0

Convert the given numeral to a numeral in base 10 1368 1368 Simplify your answer

Convert the base ten numeral to a numeral in base four 114 114 four

The function P y 0 029y2 4 007y 281 380 represents the population P in millions of people in 2005 that were years of age or older a Identify the dependent and independent variable The dependent variable is P and the independent variable is y The dependent variable is y and the independent variable is P b Evaluate P 60 P 60 Round to three decimal places as needed

Find the domain of the function f x 5x 9 tom

Write the number below as an lonic Greek numeral 5 348 Choose the correct answer below OA Etun 1 OB et n OC Tuen 1 D etun 2 B 3 Y 4 8 5 6 e f 75 8 1 90 10 1 20 K 30 A 40 50 v 60 70 o 80 T 90 9 100 P 200 300 400 D 500 600 X 700 800 900 2 2

5 Given g x 3x 6 and h x x 2 use composition to determine if g and h are inverses

Use the number line below to tell whether the segments LN and MQ are congruent 4 10 5 Are the segments LN and MQ congruent O No M to N 10

O O Use the figure to find DBF U DE Choose the correct answer below O O O ADBF ODB DB D F B E

A postulate states that any three noncollinear points lie in one plane Using the figure to the right find the plane that contains the first three points listed below Then determine whether the fourth point is in that plane Write coplanar or noncoplanar to describe the points U V X S The points U V X and S are V X Z SYU L

Write the Mayan numeral as a Hindu Arabic numeral 10 71 1 w 2 ww 11 12 ww www 13 www 14 wwww J 5 6 16 The equivalent Hindu Arabic numeral is 17 8 18 9 19

vvrite the numeral 18 570 Arabic num Which of the following is the correct answer OA TITT OB TITTI OC OD Babylonian Symbols Hindu Arabic Symbols 4 1 10

Solve the equation algebraically Verify your solution using a graphic utility x 2x 48 0 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution set is Type an integer or a simplified fraction Use a comma to separate answers as needed

Solve the equation x 16x 0 Select the correct choice below and if necessary fill in the answer box to complete your che OA The solution set is Use a comma to separate answers as needed OB There is no solution

Solve the equation 7 x 3 x 1 Select the correct choice below and fill in any answer boxes in your che OA The solution set is Simplify your answer

numeration 999 1308 Type an integer What is the equivalent Roman numeral MCCCVIII O A Choose the correct equivalent Chinese numeral below J OB O C KE O D 11

13 Find the exact value of the following be sure to show your work to receive credit a arcsin cos b 22log x c cos arccos

9 Consider the functions a Find fog 9 b Find fog x f x x 5x and g x x 7

Use a calculator to solve the equation on the interval 0 0 2 5 sin 0 2 0 What are the solutions in the interval 0 0 2n Select the correct choice and fill in any answer boxes in your choice below OA The solution set is Type your answer in radians Round to two decimal places as needed Use a comma to separate answers as needed OB There is no solution

Match the following functions with the graph a The cost of building a house as a function of its square footage b The height of a ball dropped from a 330 foot building as a function of time c The height of an animal as a function of time d The demand for energy drink as a function of price e The height of a child on a swing as a function of time a b c d Ay oo Q U IV

Find the slope and y intercept of the given line Then graph the line 1 y 6 x 1 The slope of the line is cimplified fraction

Please write the correct number in each blank to indicate that each of the following are equivalent fraction 5 9 36

In the study of heat transfer the equation 5x 2 tan x 0 occurs Graph Y 5x and Y 2 tan x for x 20 Determine the number of points of intersection of these two graphs Find the first two positiv solutions of 5x 2 tan x 0 rounded to two decimal places if they exist Which of the following graphs shows Y 5x and Y 2 tan x on the same set of coordinate axes OA Q T All graphs have x values 0 2 and y values 26 26 Determine the number of points of intersection of Y 5x and Y 2 tan x B A There are an infinite number of points of intersection OB There are two points of intersection OC There are no points of intersection OD There are three points of intersection Select the correct choice below and fill in any answer boxes in your choice and the second is x OA The first positive solution is x Round to two decimal places as needed CLE O C Q

Problem 4 1 point If there is more than one answer separate them with commas If the answer is an interval enter it in the form a b a b a b or a b Write infinity for o and infinity for co Click here for more Let f x be the polynomial f x x 7 x 6 x 2 What is the degree of the polynomial 7 For what value s of x is the polynomial equal to zero 7 2 On what interval s is the polynomial negative Note You can earn partial credit on this problem d JAI

Graph the equation using a graphing utility Use a graphing utility to approximate the intercepts rounded to two decimal places Use the TABLE feature to help establish the viewing window y 22x 23 Enter the y intercept s Select the correct choice below and fill in any answer boxes within your choice OA y Type an integer or decimal rounded to two decimal places as needed Use a comma to separate answers as needed B There is no y intercept

The graph of an equation is given to the right List the intercepts of the graph The intercept s of the graph is are the point s Type an ordered pair Use a comma to separate answers as needed

Determine the viewing window used Xmin Xmax 8 3 3

Solve the inequality algebraically Graph the solution set Verify your results using a graphing utility x 1 4 4 5 1 3 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution set is Type your answer in interval notation Use integers or fractions for any numbers in the expression

a Graph f and the secant lines passing through P 3 15 and Q x f x for x values of 4 3 5 2 5 Find the slope of each secant line To sketch the graph of f x 8x x first construct a table of values by evaluating the function f x for various values of x Consider x 4 To evaluate f x with x 4 substitute 4 for x in f x f x 8x x f 4 X 8 4 4 16 Step 2 Similarly evaluate f x for the values below and complete the table 16 4 3 5 3 2 5 2 1 5

Use the graph of F to find the given limit When necessary state that the limit does not exist lim F x X 5 Select the correct choice below and if necessary fill in the answer box to complete your choice OA lim F x X 5 Type an integer or a simplified fraction

In the given right triangle find the side labeled x X Need Help 26 Read It X 2 X