Application of derivatives Questions and Answers

n 108 Suppose that the value V of a certain product depreciates with time t where V t 120 Find lim V t 30t 16 t

Fiven the polynomial identify the coefficients and degree of each term 3x 2 7x 3x 4x First term degree Second term degree Third term coefficient 3 coefficient 2 degree 2 Fourth term degree 4 Fifth term degree 3 coefficient 4 Note make sure that you understand the terms leading coefficient and leading term What is the leading coefficient coefficient 7 coefficient 3 What is the degree of the leading term What is the degree of the polynomial

105 Find lim f x if x 1 1 f x 2 2 x 1 x 1 x 1

If f x x 5 and 2 g x x 1 find f g x 1

Math 126 Homework 9 Sects 2 7 2 8 3 12 pts a Find the inverse function of f where f x 3x 11 b Use function composition to prove that the two functions are inverses

Given the relationship between the perimeter of a square and its side length ans a On the graph below i Construct a graph on the axes below to represent the square s perimeter P in terms of its square s side length s ii Represent an increase in the square s side length from 3 cm to 4 cm iii Represent the corresponding increase in the square s perimeter Hint 22 20 18 16 62 14 12 10 8 6 4 2 P 6 S

Practice For each problem find the required composition and state the domain of the composition f x 1 h g x 2 g h x 3 h f x 1 4x 1 x g x h x x 6 x d domars

Evaluate the integral 3 sin x dx sin x dx

Evaluate the integral 2 cos 5x dx 3 2 cos 5x dx 3

Find the indicated integral if it exists 8 e8x el6x 1 dx

Find a polynomial f x of degree 4 with real coefficients and the following zeros 1 multiplicity 2 1 2i To

A function f is given and the indicated transformation is applied to its graph Write the equation for the final transformed graph f x x shift 2 units to the left

A function f is given and the indicated transformations are applied to its graph in the given order Write the equation for the final transformed graph f x x reflect in the y axis and shift upward 7 units y

The figure shows the graph of a quadratic function f x Use it to find the minimum value of f x y f x 8 8 Ay 201 18 16 14 12 10 964GJ 6964 8 2 14 1210 8 6 4 2 2 4 6 8 101214 X Q Q The minimum v Type an intege

5 Y1 is defined as a quadratic function Determine the coordinates of the vertex of the graph maximum or minimum point and value and the range of the function ww The coordinates of the vertex are Type an ordered pair 1 7 X 1 X E 10 34301 5 5

ertex and b the x intercepts y 0 29x 7x 0 37 a The vertex is Type an ordered pair Round the final answer to the nearest hundredth as needed Round all intermedia vo decimal places as needed

or the following quadratic function a use the rmula to find the coordinates of the vertex an e function x x 4x 1 he vertex is Type an ordered pair

Find a possible formula for the function represented by the data X 0 1 2 3 f x 4 80 6 72 9 41 13 17 NOTE The value for the base should be correct to one decimal place f x

For y 2x 10x d y 0 6x find 445

A town has a population of 4791 people at time t 0 The population increases by 3 per year Enter a formula for the population P of the town as a function of year t P t

Give a possible formula for the function shown in the figure below y 20 NOTE Round any calculated values to two decimal places y t 20 25 11 30 t

5 4 3 2 1 5 4 3 2 1 7 2 3 5 4 2 3 4 List all the numbers x at which the function graphed above is not differentiable Separa commas

5 4 3 2 1 V 4 3 2 1 23 3 4 L List all the numbers x at which the function graphed above is not differentiable Separate answers L commas

3 If f x 2 X Find f 3 3 x2 find f x

If f x 3x8 7x5 3x87x5 6x 5x find f x

Next question 10 1 If f x x 0 then f x Get a similar question 2 If g x 3x7 then g x 10 1 10x You can

OA The solution set is u 0 OB The solution set is OC The solution set is the set of real numbers OD The solution set is the empty set 10 5 0 y f x 7 0 10 What is the solution set of f x 0 Select the correct choice below and if necessary fill in the answer box to c your choice

olve the following inequality x 15x 54 0 The solution is Type your answer in interval notation Use integers or fractions for any numbers in the exp exact answer using radicals as needed

Sketch a graph of f x ax bx c that satisfies the set of conditions below a 0 b 4ac 0 Choose the correct answer below O A OB LEN OD

k k 5 5 The solution set is Use a comma to separate answers Type exact answers using radica

Solve for the specified variable n q y for n n HIE Type an exact answer using radicals as needed

r X 1 0 The solution set is 0 Type an exact answer using Express complex numbers in integers or fractions for any r expression Use a comma to as needed

Evaluate the discriminant and use it to determine the number of real solutions of the equation If the equati have real solutions tell whether they are rational or irrational Do not actually solve the equation 9x 18x 9 0 www Which of the following is the correct formula for the discriminant of the quadratic equation ax bx c 0 O b b 4ac O b 4ac O b b 4ac O b 4ac

ve the following equation For an equation with a real solution support your answers gr 4 9x 2x 0 EER e solution set is ype an integer or a simplified fraction Use a comma to separate answers as needed

K equation FO an equation with real solutions support the answe x 8x 9 Rewrite the equation in factored form 0 0 Factor completely

3x 21 quation For an eq ition with real utions support your answer graphicall he solution set is Type an exact answer using radicals as needed Use a comma to separate answers as needed E umbers in terms of

10 If a ball is thrown vertically upward with a velocity of 80 ft s then its height after t seconds is s 80t 16t2 a What is the maximum height reached by the ball b What is the velocity of the ball when it is 96 ft above the ground on its way up On its way down

16000 15000 14000 13000 12000 11000 10000 9000 8000 7000 6000 5000 4000 5 FA 10 15 20 25 A quadratic model C t for the cost of tuition at a small private college in dollars for t years since 1990 is C t 8 28t 269 05t 3500 Find the equation of the tangent line for tuition in 2017 y mt b where m The tangent line estimate for tuition in 2017 is and b n M

Suppose is a continuous function where f 10 6 and f 10 3 The equation of the line tangent to the graph of y f x at x 10 will be y So f x Based on this f 10 8 A solution to f x 0 is a for a close to a 10

Suppose f is a function with 7 30 and f 7 3 Using the local linearization L x at x 7 estimate the following values of f f 10 L 10 f 6 f 6 5 Samotne

5 4 3 2 5 Add Work 4 3 2 3 5 to In the above graph estimate the slope of the tangent line at x 4

Find all k such that g x k Answer x 2x x 2 if x 2 if x 2 is continuous

A pilot is flying over the ocean She determines that the angles of depression to two ships are 52 and 45 as shown in the figure below The plane is 2 miles from the ship located at point 4 How far apart are the ships Round your answer to the nearest tenth of a mile 2 mi B miles X

avi and Carmen are standing on a riverbank at points A and B respectively See the figure below Carmen is 180 meters from a house located across the ver at point C Suppose that angle A angle BAC is 55 and angle B angle ABC is 73 How far are Ravi and Carmen standing from one another Round our answer to the nearest tenth of a meter 55 44 73 180 10 1 meters X

Find the following limit x 16 8 lim x 4 x 4

Use the sign chart for y f x below to determine where f x 0 f x I 4 Choose all that apply 0 3 00 3 0 0 1 1 0 4 4 1 0 1 1 1 3 0 4 1 O 1 3 Und 1 13 110 Und 3

Determine the derivative of f z 2e 1

Determine the derivative of f x 1 5

Consider a triangle ABC like the one below Suppose that A 112 B 36 and c 60 The figure is not drawn to scale Solve the triangle Round your answers to the nearest tenth If there is more than one solution use the button labeled or C a b 0 or X No solution

Determine the derivative of the function f x 225 3e6e