Application of derivatives Questions and Answers

lear Part 1 of 2 Solve the system of equations graphically If the does not have a single ordered pair as a solution whether the system is inconsistent or dependent y x 1 y 5x 1 se the graphing tool to graph the system

2 02 57 48 Skipped Minimize C subject to and 15x 17y 7z 11x 13y 20z 2 59 12x 9y 10z 118 x 20 y 2 0 a What is the optimal value of x 0 000 b What is the optimal value of y ptimal z 0 000 O Show Transcribed Text

S lve the exponential equation Write the exact answer with natural logarithms and then approximate the result correct to three decimal places 51 6 Select the correct choice below and if necessary fill in the answer boxes to complete your choice OA The exact answer s with natural logarithms is are x Type an exact answer in simplified form Type an integer or a fraction Use a comma to separate answers as needed The approximate answer s is are xx Simplify your answer Type an integer or a decimal Round to three decimal places as needed Use a comma to separate answers as neede B There is no solution The solution set is the empty set

Find a positive angle less than 360 that is coterminal with the given angle 145 A positive angle less than 360 that is coterminol with

d Attempt 1 ion 3 0 5 points isten ermine the dimensions of the rectangle of largest lateral triangle of side L 9 cm if one side of the gle Round your answer to the nearest tenth

Find the remaining sides and angles of the triangle ABC with right angle at C B 72 b 6 1 A a Type an integer or decimal rounded to one decimal place as needed C Type an integer or decimal rounded to one decimal place as needed

stion 1 0 5 points Listen rectangular storage container with an open top is to ngth of its base is twice the width Material for the ba eter Material for the sides costs 5 per square meter aterials for the least expensive such container Roun ecimal places 152 40

ed Salad Attempt 1 T J CIII I CI Question 4 0 5 points Listen A piece of wire 10 m long is cut into two pieces the other is bent into an equilateral triangle How square so that the total area enclosed is a minim nearest hundredth

Equations Solve the system of equa pingle ordered pair as as

1 6 10 Functions and Their Graphs Determine whether the graph is a function If it does repr give its domain and range A The domain is Type an inequality or a compound inequality The domain is all real numbers

1 Tanisha Vizquez owns a wallpaper hanging business C 15 0 25s where s is the number of square feet

pose the correct answer Intellectual property is protected by patent warranty and waiver laws patent trademark and copyright laws O trademark copyright and consumer protection laws Opatent copyright and consumer credit law

23 What is the length of the major axis of the ellipse 73 x 3 y 2 1 7 3 1

If 5 24 then 3 Estimate your answer to two decimal places

For what value of k will the polynomial P x x 3 x kx S have the same remainder when it is divided by x 3 and by x 4 X 2019 fam20 IN Nosited 2 0 K

standing top of a 14 14 ft close to the edge on vertically upward building throws a ball 7 quadratic function h t 16t 128 144 A person models balls height about the ground h t in feet t seconds after it was thrown What s the max height seconds does it take until reaches the ground How many the ball reaches the

with form axp points 340s and A power function passes through the 4 1280 Find the constants a 12 16 21 p 10 EL X o Y J 2 ticts NS XMS and P TE 19

Arif s backyard is 22 by grass of uniform width

What are the asymptotic discontinuities of the function x 3x 7

Show that there is a number x such that sin x x 1 by filling in the details of the following argument Define f x sin x Then f a 0 for a f b 0 for b 4 3 1 3 2 1 0 21 x 1 which is graphed below 1 2 Since f x is continuous by the Intermediate Value Theorem there is a number c where b c a such th f c 0 QED Now find a value of c such that sin c differs from c 1 by less than 0 1

Z Suppose f x y z z y z t 4t 1 1 y t 2 t 1 cost and z t 2 ln t t 1 Which of the following represents the dot product formulation of the chain rule for at t 0 769 1 64 1 2 0 O 2 1 2 0 1 4 O 6 1 1 4 2 2 O 6 1 1 1 2 0 O 2 2 1 1 3 3 F

14 f x x x 1 x 4 End Behavior Model Degree Leading Coefficient End Behavior use limit notation y intercept Zero 5 4 3 2 Multiplicity 1 2 Bounce or Cross 3 4 5

13 f x 3 x 2 x 1 x 4 End Behavior Model Degree Leading Coefficient End Behavior use limit notation y intercept 5 Zero 3 2 Multiplicity 1 2 3 Bounce or Cross 4 5

Consider the following function h x x 5 9 Step 3 of 4 Find two points on the graph of the parabola other than the vertex and x intercepts Answer How to enter your answer opens in new window 4

Suppose f x y z 2 y I y t 2 t 1 cost and z t 2 ln t t 1 Which of the following represents the dot product formulation of the chain rule for att 0 dt 0 769 64 1 2 0 O 2 1 2 0 1 4 O 6 1 1 4 2 2 O 6 1 1 1 2 0 O 2 2 1 1 3 3 z t t 4t 1

what is the coordinate of the vertex for given quadratic function and which way f x opens f x 2x 4x 3 2 3 opens upward 2 3 opens downward O 2 19 opens downward none of these answers Question 2

Quadratic function y is given below in vertex form What is the vertex and axis of symmetry for it y 2 x 3 1 3 1 x 3 3 1 x 3 1 3 x 1 none of these answers

1 y x x Find any local max or min and critical points using the first derivative tes

Form a polynomial who Zeros 3 3 2 d

Consider the following function g x x 3 x 5 16 Step 3 of 4 Find two points on the graph of the parabola other than the vertex and x intercepts Answer How to enter your answer opens in new window

follows f x og x or fog x the later is a short hand notation 1 What f x o g x is equal to 2 What g x o f x is equal to 3 what do have to do to find fog 2

Note Zero for y x 2 IS 2 Zero for y x 2 3 is 2 However we say its multiplicity is 3 which is the power of x 2 factor So multiplicity of a zero is the power of the factor that gives that zero in this case it is power of x 2 1 We know Y x 2 x 1 has two zeros 2 and 1 1a what is multiplicity of 2 as a zero for above y why 1b what is multiplicity of 1 as a zero for above y why 2 what are zeros and their multiplicity for y 2 x x 4 5

Complete the table after finding a simplified form of the difference quotient For the function f x complete the table below O O 4 2 4 1 40 1 4 0 01 Round to four decimal places Hint Find the difference quotient at x 4 first h x 4 2 4 1 X h 40 1 10 01 h 2 4 1 4 01 10 01 f x h f x h 1 01 4001 W ix h f x h 0 3333 0 1667 0 0167 0 0017 fix h f x 0 6667 OS 0 9756 0 9975 tx h f x h 0 1667 0 2 0 2439 0 2191 0 166

Macmillan Learning What is the name of the comp name What is the name of the con

Graph the equation and state the slope of the line if t y 8

The Schwimmers cost for cable televisi of months of service Complete parts a

se the quadratic formula to solve the eq 5x 7x 3 0

Solve the equation by factori 3x 7x 2

You have made a quilt that is 4 feet by 5 feet You are going to add a decorative border of uniform width You want the quilt with border to have a total area of 90 feet2 What should be the width of the border Part a Write a quadratic equation set equal to zero that you could use to determine the width of the border feet Part b The width of the border should be

a graphing utility to approximate the local maximum v ing a graphing utility graph the function for 6 x 4 A 0

Use the second derivative test to find the relative maxima and minima of the given function f x x 32x 7 O min at 0 7 max at 4 249 O max at 0 7 min at 4 249 O min at 4 249 max at 0 7 min at 4 249 O max at 4 249 min at 0 7 max at 4 249

Use first and second derivative information to sketch the graph of the function f x 2x5 10x 7 O t

The graph of a function is shown below Choose the graph A B C or D that could be the graph of the derivative of the function

The graph off has a relative minimum Part 2 of 3 b Use interval notation to write the intervals over which fis increasing or decreasing The graph of fis increasing on the interval 5 00 Part 2 3 Part 3 of 3 of 9 8 at x 5 The graph of fis decreasing on the interval

Find the intervals of increase and decrease for the given function f x x 4x 3 f x is increasing for x 2 f x is decreasing for x 2 Of x is increasing for x 3 and x 1 f x is decreasing for 3 x 1 f x is increasing for x 2 f x is decreasing for x 2 Of x is increasing for 3 x 1 f x is decreasing for x 3 and x 1

Specify the intervals on which the derivative of the given function is positive and those on which it is negative O f x 0 for x 1 and x 1 f x 0 for 1 x 1 O f x 0 for x 0 f x 0 for x 0 O f x 0 for x 0 f x 0 for x 0 O f x 0 for 1 x 1 f x 0 for x 1 and x 1

Use implicit differentiation to find the second derivative x 2y 5 O 5 O 2 2 O 5 41 322 2 213 dx

Use a graphing utility and the following graph to answer the questions below f x 0 3x 1 2x 2x 1 Part 0 3 Part 1 of 3 a Find the locations and values of the relative maxima and relative minima of the function on the standard viewing window Round to 3 decim The graph off has a relative maximum of The graph of has a relative minimum of at x at x

Part 0 2 Part 1 of 2 4 o The function has no relative minimum The function has one relative minimum The function has two relative minima A relative minimum occurs at the point s 0 0 00 X

1 2 3 Part 0 2 4 51 5 6 Identify the location and value of any relative maxima or minima of the function 7