Application of derivatives Questions and Answers

Use Descartes Rule to determine which of the following is a possible number of solutions for the function f x x 2x x 1 Select all that apply 3 positive 0 negative and 0 imaginary 1 positive 2 negative and 0 imaginary 2 positive 1 negative and 0 imaginary 1 positive 0 negative and 2 imaginary 0 positive 3 negative and 0 imaginary 0 positive 1 negative and 2 imaginary

Given the triangle below find cot 0 Enter your answer as a ratio of sides 24 25 7

The matrix A 26 21 28 23 Find its eigenvectors For 5 the eigenvector is and for 2 the eigenvector is has eigenvalues 5 and 2

1 point Given the matrix 3 3 2 2 2 3 1 30 find its determinant Do not use a calculator The determinant is

1 point Find the determinant of the matrix det A 3 A 341 9 2

Given the triangle below find sec 0 Enter your answer as a ratio of sides 0 41 40 9

Find the angle in degrees between 0 and 360 which intersects the unit circle at the point 1 Do not include the degree symbol in your answer For example if the answer was 20 you would enter 20 power below

Using Descarte s Rule of Signs which are possible combinations of zeros for f x 2x4 8x 12x 16x 10 Select all that apply 4 positive 0 negative 0 complex 2 positive 0 negative 2 complex 0 positive 4 negative 0 complex 2 positive 2 negative 0 complex 0 positive 0 negative 4 complex

Graph the function f x log x There is one point that can be moved You can only graph integer points for example you cannot plot the point above and below the x axis as needed Do not move either point off of the graph as you will not be able to click on the point again Provide your answer below 2 1 2 0 2 2 3 4 5 6

1 Find all solution in 0 2x a cos2x sinx 1 b cos x 2 cos x 3 c cos2xsinx sinx 0 d sec x 2tan x 0

Here is a graph of the function f 5 3 2 2 3 2 3 Use the graph to find the following If there is more than one answer separate them with commas a All values at which has a local minimum b All local minimum values of f

1 Given that f x x 2x and that g x x 15

Find the equation of the exponential function whose graph is shown below Provide your answer below 12 18

Find the possible numbers of positive and negative real zeros for the function f x 2x4 10x 11x 15x 12 1 Select the correct answer below 4 2 or 0 positive real zeros 4 2 or 0 negative real zeros 4 2 or 0 positive real zeros 0 negative real zeros 0 positive real zeros 4 2 or 0 negative real zeros 0 real zeros

Consider the function f x 2x4 2x 6x 7x 2 Using Descartes Rule of Signs what is the maximum possible number of positive roots

The function y e 3x is vertically stretched by a factor of 4 reflected across the y axis and then shifted up 5 units find the resulting function Sorry that s incorrect Try again

the f x by dragging the blue points to the locations on the x axis that correspond to the zeros of the function Use the red point as a slider to select the number of zeros that your graph will show You may click on a point to verify its coordinates Provide your answer below 10 5 200 100 0 100 f x 2 x 5 x 1 x 8 10

f t dt 2 and f t dt then 0 5 01 0 1 05 20 f t dt 3

A bacteria culture starts with 1000 bacteria and the growth rate is proportional to the number of bacteria After 1 hour the population is 3000 a Find an expression for the number of bacteria after t hours b Find the number of bacteria after 2 hours O a P t 1000 4 b 16000 O a P t 1000 3 b 9000

Determine whether the improper integral converges or diverges If it converges find its value fi dz O Diverges O Converge 1 O Converge 2 O Converge

Find the indefinite integral f O In C O In C O In C Oln C 3 x x 2 da

Evaluate the integral fx sin x da Cos 1 1 2 COS 2 O sin 1 O 1 cos 1 2

zation Problems Question 5 4 5 27 Part 1 of 2 HW Score 69 23 9 of 13 points Points 0 of 4 A boat on the ocean is 5 mi from the nearest point on a straight shoreline that point is 15 mi from a restaurant on the shore A woman plans to row the boat straight to a point on the shore and then walk along the shore to the restaurant Complete parts a and b below COLLE a If she walks at 3 mi hr and rows at 2 mi hr at which point on the shore should she land to minimize the total travel time miles from the restaurant To minimize the total travel time the boat should land Type an exact answer using radicals as needed

An archer releases an arrow with an initial velocity of 30 feet per second at a height of 3 feet The patffthe arrow takes can be modeled using the function f x 16x 30x 3 where f x represents the height in feet of the arrow and x represents the time the arrow travels in seconds How many seconds until the arrow hits the ground Round your answer to the nearest hundredth if necessary Do not include units in your answer Drouide

As x approaches negative infinity for which function does f x approach negative infinity Select all that apply Select all that apply f x 4x 1 3x 5 x 2 f x 4 8x 2x 3 x 9 x 5 f x 4x 3 x 5 x 8 x 3 f x 0 5x 3x 7 4x 1 x 9 x 3 f x 0 2x x 4 x 7 x 8 x 2 x 1 f x 9x 1 3x 4 2x 5 x 8 x 2

Question The flight of a kicked football follows the quadratic function f x 0 02x 2 2x 2 where f x is the vertical dista in feet and x is the horizontal distance the ball travels How far in feet will the ball travel across the field by the time it F the ground Round your answer to one decimal place Provide your answer below

Describe the end behavior of the function f x 3x4 19 Provide your answer below f x goes to As r goes to f x goes to

Which of the following is a polynomial function Select all correct answers Select all that apply f x 3x 4x 5x 3 f x x x 3x 2 f x 2 14 f x 4 20 2

A ball is launched directly in the air at a speed of 40 feet per second from a platform located 10 feet in the air The motion of the ball can be modeled using the function f t 16t 40t 10 where t is the time in seconds and f t is the heig of the ball When in seconds will the ball hit the ground Write your answer to the nearest hundredth of a second Do not include units in your answer Provide your answer below

A ball is thrown upward and outward from a height of 8 feet The height of the ball f x in feet can be modeled by f x 0 3x 2 1x 8 where x is the ball s horizontal distance in feet from where it was thrown Use this model to solve parts a through c a What is the maximum height of the ball and how far from where it was thrown does this occur The maximum height is feet which occurs feet from the point of release Round to the nearest tenth as needed b How far does the ball travel horizontally before hitting the ground feet Round to the nearest tenth as needed c Graph the function that models the ball s parabolic path Choose the correct graph below O A Height 25 20 15 10 5 0 0 5 10 152025 Horizontal Distance Q G B Height 25 20 15 10 5 0 0 5 10 15 20 25 Horizontal Distance oo G C Height 25 20 15 104 5 04 0 5 10 152025 Horizontal Distance Q D Height 25 20 15 104 5 0 0 5 10 15 20 25 Horizontal Distance Q Q

Points 0 of 4 A boat on the ocean is 5 mi from the nearest point on a straight shoreline that point is 6 mi from a restaurant on the shore A woman plans to row the boat straight to a point on the shore and then walk along the shore to the restaurant Complete parts a and b below 5 mi 6mi To minimize the total travel time the boat should land miles from the restaurant Type an exact answer using radicals as needed Save a If she walks at 3 mi hr and rows at 2 mi hr at which point on the shore should she land to minimize the total travel time

An auditorium with a flat floor has a large screen on one wall The lower edge of the screen is 3 ft above eye level and the upper edge of the screen is 10 ft above eye level see figure How far from the screen should you stand to maximize your viewing angle 10 ft 3 ft X 0 You should stand ft from the screen to maximize your viewing angle Type an exact answer using radicals as needed

A rectangular tank with a square base an open top and a volume of 10 976 ft is to be constructed of sheet steel Find the dimensions of the tank that has the minimum surface area The tank with the minimum surface area has a height of with a side length of ft ft and a square base

a Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 7 ft by 5 ft The resulting piece of cardboard is then folded into a box without a lid Find the volume of the largest box that can be formed in this way b Suppose that in part a the original piece of cardboard is a square with sides of length s Find the volume of the largest box that can be formed in this way a The maximum volume of the box is approximately Round to the nearest hundredth as needed ft

the Draw the function f x by dragging the blue points to the locations on the x axis that correspond to the zeros of function Use the red point as a slider to select the number of zeros that your graph will show You may click on a point verify its coordinates Provide your answer below 40 30 20 10 0 10 20 f x 4 x 1 x 2 x 5 10

A single card is selected from an ordinary deck of cards The sample space is shown below Find the probabilities Enter the probabilities as fractions a 1 4 47 ND P club and a king b P club or a king 200 Hearts red cards Diamonds red cards 44 N Spades black cards Clubs black cards

Consider the ollowing table showing the results of a survey of TV network executives Opinion of Current Programming Network Satisfied S Not Satisfied S Total 18 30 22 35 15 30 95 NBC N CBS C ABC A Total 55 2259 12 13 15 40 uppose one network executive is selected at random Find the indicated probabilities Round your answers to four decimal places a What is the probability that it is an NBC executive b What is the probability that the selected person is satisfied c What is the probability the selected person is from CBS if we know the person is satisfied with current programming d What is the probability the selected person is satisfied if we know the person is from CBS

1 point Compute the following products 7 9 9 6 3

1 point Compute the following product 9 3 57 2 10 5 9 6 6 19 6

ect the correct answer below The polynomial has degree at least 5 The polynomial has degree at most 5 The polynomial has degree at most 4 The polynomial has degree at least 4 6 5 LLI 4 4321 7 6 5 4 3 2 1 11 2 3 4567AWNH 4 5 6 7 2 3 4 567

x x 4x 4 0 3 To solve the inequality using a graphing utility first graph the function f x x x 4x 4 Choose the correct graph below A B 5 5 1 by 10 10 1 E The solution set is Type your answer in interval notation 5 5 1 by 10 10 1 Q OU OC 5 5 1 by 10 10 1

Three coins are tossed Consider the odds against getting three heads How many different outcomes are possible outcomes How many of the possible outcomes are three heads outcomes How many of the possible outcomes are not three heads outcomes What are the odds against getting three heads

Which of the following are binomials Select all correct answers Select all that apply 3x y 3x 3x y 3x 3x y z 2x yz 3xy 2x y z 3xyz

16 8 points Use the method of Lagrange multipliers to find the points on the surfa r yz 4 closest to the origin

Find the degree of the following polynomial 5 x 3x x

Find the leading coefficient of the following polynomial 5x 7x 6

Find the degree of the following polynomial 5x 7x 6

20 points Find the matrix exponential e for the given system 21 t 0 2 5 3 t 00 2 Then use it to find a solution satisfying the initial condition 7 0

Write the following numbers in the polar form re 0 0 2 1 8 a T b 7 7i T c 3 3i T 0 0 0

Find all the real zeros of the following polynomial Provide your answer below f x x6 1000x