Application of derivatives Questions and Answers

What function represents the amount of change given from a 10 bill f x based on x the number of bagels purchased

the predicted population of a certain city is given by P 50 000e 0 15 where y is the number of years after 2020 What is the population in the year 2040

The average cost for a company to produce x units of a product is given by the function A x estimate the change in average cost as production goes from 200 units to 201 units The change in average cost is approximately dollars 13x 400 X Use A x

Let R x C x and P x be respectively the revenue cost and profit in dollars from the production and sale of x items If R x 8x and C x 0 004x 2 5x 50 find each of the following a P x b R 150 C 150 and P 150 c F x C x and P x d R 150 C 150 and P 150 a P x Use integers or decimals for any numbers in the expression b R 150 Type an integer or a decimal C 150 Type an integer or a decimal www P 150 Type an integer or a decimal c R x Type an integer or a decimal C x

Use the Laws of Logarithms to evaluate the expression log2 10 log2 30 log2 48

Raggs Ltd a clothing firm determines that in order to sell x suits the price per suit must be p 160 0 75x It also determines that the total cost of producing x suits is given by C x 2500 0 5x a Find the total revenue R x b Find the total profit P x c How many suits must the company produce and sell in order to maximize profit d What is the maximum profit e What price per suit must be charged in order to maximize profit a R x b P x c suits d The maximum profit is per unit must be

Use the Laws of Logarithms to combine the expression 9 log x 3 log x 1

Use the Desmos graph Limits and Continuity Informal to answer the following questions Drag the blue point currently located at 3 2 to 3 1 You may also use the numerical slider for a After making this adjustment to the Desmos graph the numerical value of the limit at x 3 from the left is Y After making this adjustment to the Desmos graph the numerical value of the limit at x 3 from the right is y After making this adjustment to the Desmos graph the value of the function at x 3 is y By using the slider for o or dragging the red point currently located at 5 2 explore the graph as decreases from 5 to 2 Which of the following is true about the function at x 3 Select an answer

A sporting goods store sells 125 pool tables per year It costs 14 to store one pool table for a year To reorder there is a fixed cost of 35 per shipment plus 15 for each pool table How many times per year should the store order pool tables and in what lot size in order to minimize inventory costs The store should order pool tables times per year to minimize inventory costs

Use the Laws of Logarithms to expand the expression log4 7xy

Use the Laws of Logarithms to expand the expression log7 AB6

Use the Laws of Logarithms to expand the expression 9x log 3x

Use the Laws of Logarithms to expand the expression log 5

Use the Laws of Logarithms to evaluate the expression log 243

Use the Laws of Logarithms to evaluate the expression 12 21 log3 9

1 point Assignment 6 Problem 4 Find the volume of the solid obtained by rotating the region enclosed by y x y 25x x 0 about the line y 0 using the method of disks or washers Volume Note You can earn 5 for the upper limit of integration 5 for the lower limit of integration 40 for the integrand and 50 for the finding the volume If you find the correct volume you will get full credit no matter what your other answers are

Select all the points at which the graph above is not differentiable 1 4 3 2 0 a 2

In the following questions consider the function Enter DNE if an answer does not exist a Give the domain of f in interval notation b Determine the intervals on which f is concave up down f is concave up on f x 8 si f is concave down on c Based on your answers in a and b determine the inflection points of f help numbers Each answer should be entered as an ordered pair x y Separate multiple a d Find the critical numbers of f and use the Second Derivative Test when poss Relative maxima occur at x Separate multiple answ Relative minima occur at x Separate multiple answe

Consider the function f x Its derivative is f x Its second derivative is f x x 2 A The graph that correctly displays f x in black and f x in orange is OAOBOCOD f is conco B help formula D Using the graphs of f and f indicate where f is concave up and concave down Enter f is concave up on help intervals

Complete the table to determine the effect of the num for 14 yr under the following compounding options Ro nearest cent Compounding Option n Value 1

f x x 9x 21x 1 Enter DNE if an answer does not exist a Give the domain of f in interval notation intervals b Determine the intervals on which f is concave up down f is concave up on f is concave down on Based on your answers in a and b determine the inflection points of f help numbers Each answer should be entered as an ordered pair x y Separate multiple answers with commas d Find the critical numbers of f and use the Second Derivative Test when possible to determine the relative extrema Relative maxima occur at x help commas Relative minima occur at x commas e Find the x values where f x has a relative maximum or minimum f has relative maxima at x commas f has relative minima at x commas Separate multiple answers with Separate multiple answers with Separate multiple answers with Separate multiple answers with

Let f x 2x 3 if I 5 344z if I 5 2 if x 5 Determine whether f x is continuous at x 5 If f x is not continuous identify why Not continuous lim f x f a z 5 Not continuous f 5 is undefined Not continuous lim f x does not exist Z 5 The function is continuous at x 5

Let f x 52 5 if 5 504x if 5 27 if 5 Determine whether f x is continuous at x 5 If f x is not continuous identify why Not continuous lim f x does not exist 2 5 Not continuous lim f x f a 5 Not continuous f 5 is undefined The function is continuous at x 5

The graph below is the function f x 54 4 3 2 5 4 3 2 1 lim How Hu 2 HIG P O 2 Lag Determine which of the following explains why continuity is violated at x f x does not exist f x and f a exist but are unequal Aurt lim HIP Of a is not defined

AV SVILes by Ltducation Los An 2 Hwk Ob 1 4 question 20 of 20 1 point Question Attempt 1 of 3 of 4 10 11 12 13 ulation of a country in 2010 was approximately 34 million with an annual nated by P t 34 1 00806 where t is the time in years since 2010 exponential function the graph of P an increasing or decreasing exponential function raph of P is an increasing In

Part 1 of 6 a As x 00 f x 3 Part 2 of 6 b Asx 2 f x Part 3 of 6 c As x 2 f x 00 Part 4 of 6 d As x f x 3 Part 4 6 Part 5 of 6 complete the statement y f x e The graph is decreasing over the interval s Give your answer in Interval notation Select Never decreasing if applicable 0 0 0 0 0 0

Use the function below to answer the following questions 3 a Use transformations of the graph of y Part 0 3 1 Part 1 of 3 b Write the domain and range in interval notation c Write an equation of the asymptote BODETAA to graph the given function a Use transformations of the graph of y 1 to graph the given function X 5

Graph the function and write the domain and range in interval notation f x 3 Part 0 2 Part 1 of 2 Graph the function f x 3 D

Answer the following questions about the graph of f based on the graph of f above A State the x values over which f is positive 1 U 1 0 U 2 00 B State the x values over which f is negative 0 2 C State the x values over which f is zero 0 2 D State the x values over which f is undefined 1 0 13 1 pt X X

Express the equation in exponential form a log3 9 2 b log3 1 0

Graph the feasible region for the following syste x y 2 x y 3

Graph the feasible region for the following sy

y 1 By 2 Question 2 12 gmented matrix of the given syste

Find an equation of the tangent line to the curve a lemniscate at the point 3 1 2 x y 25 x y An equation of the tangent line to the lemniscate at the given point is

The volume of a right circular cylinder of radius r and height h is V h a Assume that r and h are functions of t Find V t b Suppose that r e4t and h e8t Use part a to find V t c Does the volume of the cylinder of part b increase or decrease as t increases a Find V t Choose the correct answer below OA V t 2 r t h t h t r t r t OC V t r t h t b V t

48 Change the point 1 1 from rectangular to polar coordinates A 2 315 B 2 135 C 2 315 D 2 225

41 Write one pair of polar coordinates that name the point with coordinates 8 200 restricting 8 so that 360 e 360 What is one of the answers A 8 20 B 8 290 O C 8 110 D 8 160

35 Find the square roots of 36 cos 152 i sin 152 Leave your results in polar form What is one of the answers A 6 cos 31 i sin 31 B 6 cos 166 i sin 166 C 6 cos 76 i sin 76 D 6 cos 121 i sin 121

9 Solve for x in the equation x4 81 0 Leave your results in polar form What is one of the answers A B 3 cos 225 i sin 225 C 3 cos 247 30 i sin 247 30 3 cos 180 i sin 180 OD 3 cos 202 30 i sin 202 30

40 Solve for x in the equation x4 81 0 Leave your results in polar form What is one of the answers OA 3 cos 315 i sin 315 B 3 cos 292 30 i sin 292 30 C 3 cos 337 30 i sin 337 30 D 3 cos 270 i sin 270

45 Describe the graph of the equation r 6 A a line passing through the pole and through the point 6 0 B a line perpendicular to the polar axis passing through the point 0 OC a circle of radius 6 with center at the point 6 0 a circle of radius 6 with center at the pole D

32 Divide and express your result in algebraic form a bi 8 cos 250 i sin 250 2 cos190 i sin 190 OA 2 3 3 OB 2 2 3 OC 2 21 3 2 3 3 D

29 Change 2 cos 210 i sin 210 to rectangular algebraic form A 1 3 B 1 3 C 3 i D 3 i

26 Simplify 1 i 2 3 i A 1 5i B 1 i O C 5 i D 5 5i

16 W Notice this is the graph of the derivative of g NOT the graph of g itself Answer the followi questions about the graph of g based on the graph of g above A State the x values over which g is positive B State the x values over which g is negative C State the x values over which g is zero 0 1 D State the x values over which g is undefined

1 Match the graphs with the functions i f x y x y ii g x y x y

roblem 1 Find the volume of the solid bounded by the graphs of r 3 sin 30 z 8 x y z 0 in the first octant

If the derivative f x is positive increasing concave down Then the function f x is not all info may be used increasing concave down increasing concave up decreasing concave down decreasing concave up

If a function f x is negative decreasing concave up Then its derivative f x is not all info may be used positive decreasing negative increasing positive increasing negative decreasing

7 6 5 4 3 2 7 1 00 00 1 00 1 00 00 6 5 41 3 10 2 23 4 6 7 4 5 G 7 Over which interval of x values is f 0 1 00 1 00 00 1 00 1 00 00 Over which interval of x values is f 0 1 00 Over the interval 00 00 this function is