Application of derivatives Questions and Answers

Previous Proble 1 point Water constant rate T the water is 4 0 Your answer

Previous Problem Pro 1 point A spherical snow diameter is 18 cm Your answer Hint The volume of a sph

Siven the g x P x 2 3x 2 x 4 x 2 x 6 What are the equations of the asymptotes of the function Determine if there are any points of discontinuity Explain why or why not Describe the end behavior as x approaches o and as x approaches 00 ED

Find the vertical asymptote s of the graph of the function f x 4 x x 5 x 4

Function g x 2x 8 For x 0 the inverse function is f x V x 4 For x 0 the inverse function is d x x 4 8 0 10 f x 0 S d x q 2 t q r S t

27 28 Find the exact area of the surface obtained by rotating the given curve about the x axis 27 1 1 x Srs

9 16 Find the exact area of the surface obtained by rotating the curve about the x axis 9 y x 0 x 2 11 y x 1 0 x 3 10 y 5 12 y 1 e 0 x 1 x 3 x 5

1 Find a value of c such that the conclusion of the mean 3 value theorem is satisfied for f x 2x 6x 2 on the interval 2 21

9 24 Find the exact length of the curve 9 y x 2 0 x 2 10 y x 4 2 0 x 4 11 y 1 x 2 0 x 1 12 36y x 4 2 x 3 13 y 14 x X 3 3 4 y 8 1 4x 1 4y 5 1 x 2 1 y 2 y 0 15 y In sin 2x 8 x TT 6 2

POSSIBLE POINT Identify if the function has a point of discontinuity oblique asymptote one vertical asymptote horizontal asymptote OR two or more vertical asymptotes Select ALL that apply f x 2 x x 2 x 1 Point of Discontinuity Oblique Asymptote One Vertical Asymptote Horizontal Asymptote OTwo or More Vertical Asymptotes

POSSIBLE POIN Identify if the function has a point of discontinuity oblique asymptote one vertical asymptote horizontal asymptote OR two or more vertical asymptotes Select ALL that apply f x x 2x8 x 3x 4 Point of Discontinuity Oblique Asymptote One Vertical Asymptote O Horizontal Asymptote Two or More Vertical Asymptotes

Dave borrowed 600 on January 1 2006 and paid it all back at once on December 31 2006 The bank charged him a 5 00 service charge and interest was 44 20 What was the APR Do not round intermediate calculations Enter your answer as a percent rounded to 2 decimal places Annual percentage

If 1500 square centimeters of material is available to make a box with a square base and an oper top find the largest possible volume of the box Volume cubic centimeters

The sum of one positive number and the square of another equals to 6 Choose the numbers so that their product is as large as possible Enter the exact value of the product of the two numbers The maximal value of the product is

a red b 28 Probabilities in Dart If a dart hits the squa shown here at random the probability that it w colored region Hint

is function is not one to one and must have the domain restricted Restrict the domain of the function f so that the function is one to one and increasing What is the domain f x

Without using a calculator find the exact value of sec 2 Give your angle in radians use pi for TT

A culture of bacteria has an initial population of 94000 bacteria and doubles every 6 hours Using the formula P Po 2 where Pt is the population after t hours Po is the initial population t is the time in hours and d is the doubling time what is the population of bacteria in the culture after 19 hours to the nearest whole number

Find dy dx dy if y dx 5 sec x x3 You need not simplify your answer

e graph of the derivative f of a function f is shown YA 0 2 y f x 4 6 AX

25 26 Find the length of the arc of the curve from point l to point Q 25 y x P 1 Q 1 1

Let f x 8 cos x 9 tan x f x f 4 3 Round your answer to the nearest hundred

If 0 1T then find exact values for the following 6 sec 0 equals csc 0 equals 2 tan 0 equals cot 0 equals 2 3 1 3 3 D from h X OF Our Or

Compute the gradient of the following function and evaluate it at the given point P 2 2 g x y x 7x y 5xy P 2 1 2 The gradient is Vf x y 0

5 Find the dimensions of a rectangle with perimeter 100 m whose area is as large as possible

11 If 1200 cm of material is available to make a box with a square base and an open top find the largest possible volume of the box

7 Crop yield A model used for the yield Y of an agricultural crop as a function of the nitrogen level N in the soil mea sured in appropriate units is Y kN 1 N where k is a positive constant What nitrogen level gives the best yield

Morgan Wilson Complete the Square Part 1 of Method Mar 22 9 04 36 AM What is the intermediate step in the form x a 2 b as a result of completing square for the following equation 3x 2 33 48x

An rock s acceleration at time t is given by a t 16t and its initial velocity is 35 Find the velocity function v t Ov t 16t 35 Ov t Ov t Qu t F 8t 35 8t 35t 35t 16

Find f x if f x O 28x 5 3 7 19 1 x 1 2x 3 1 3 2 O O 28x5 32 O 7 x4 3 3 and f 1 4

2 Consider the function f x y 6 3 y whose graph is a paraboloid see figure X a Find the value of the directional derivative at the point 1 1 in the direction 2 2 2 b Sketch the level curve through the given point and indicate the direction of the directional derivative from part a a The directional derivative is Type an exact answer using radicals as needed

The function f x 5 9z 144 has one local minimum and one local maximum This function has a local maximum at with value and a local minimum at x with value

5 4 3 2 1 2 23 q The function graphed above is Increasing on the interval s est Decreasing on the interval s

Could the three graphs be antiderivatives of the same function

3 Match the function with its graph try wit f x log x f x log x A y 2 B y

Find c so that ET n 1 1 c n 11 4

Evaluate the given series 8 n 7 12 n 3n

Consider the sequence an a Evaluate the limit below lim an n x b Evaluate the given series n 1 an 4n 15 2n

Suppose there exists a population where 85 of its members possess a certain characteristic Let be the proportion of a random sample of 342 members that also possess that certain characteristic Determine the following probabilities Round solutions to four decimal places if necessary Find the probability that the sample proportion is less than 0 87 P p 0 87 Find the probability that the sample proportion is between 0 78 and 0 85 P 0 78 p 0 85

According to a recent study more than 900 people move to Florida each day In fact data show that only 34 of current Florida residents were born in Florida Let p be the proportion of people who were born in Florida out of a random sample of 261 Florida residents Determine the following probabilities Round solutions to four decimal places if necessary Find the probability that in a random sample of 261 Florida residents greater than 43 were born in Florida P p 0 43 Find the probability that in a random sample of 261 Florida residents between 35 and 40 were born in Florida P 0 35 p 0 4

Score 100 Circle answers and show all steps NEATLY Each problem is 5 points unless otherwise labeled No calculators If a formula or method is specified you must use that method or you get no points I have read these instructions Initial here 1 7 1 Example 4 Verify the identity working only the Right Hand side Show all steps 2 tan x secx 1 1 sin x 1 1 sin x 2 7 2 5 Use an addition or subtraction formula to find the exact value of the expression cos 105

X Consider the function f x y 6 y whose graph is a paraboloid see figure 6 a Find the value of the directional derivative at the point 3 0 in the direction 2 21 a The directional derivative is Tyne an exact answer using radioalo www

10 Find the Taylor polynomial P4 for f x In x at xo 1 1 x 1 x 1 x 1 x 1 4 1 1 x 1 x 1 x 1 x 1 a b c 1 d x D x 1 x 1 x 1 1 x 1 x 1 x 1 x 1 4

Use transformations to graph the function Determine the domain range horizontal vertical asymptote and intercept s of the function a h x 2e x 1 b f x log x 5 1

Next question The function f x 8x 5x has one local minimum and one local maximum Algebraically use the derivative to answer the questions Leave answers in 4 decimal places when appropriate this function has a local maximum at x with value 32 Get a similar question You can retry this qu and a local minimum at x 1 5 21 2 X 1 5 2 2 OF

Get a similar question You can retry this quest I 1 4 HHH 2 2 Give the ordered pairs in decimal form and separate with commas if necessary Point s of inflection 40 14

Find the local quadratic approximation of f x x at xo 1 and use that approximation to find the approximation of 1 03 a 1 092727 b 1 0927

4 3 2 Add Work 1 q The function graphed above has an inflection point x

2 Use sigma notation to write the Taylor series about Xo 1 for Inx

di 4 H 2 2 Give the ordered pairs in decimal form and separate with commas if necessary 1 4 dr 54