Application of derivatives Questions and Answers

Graph each function and identify its key characteristics 1 1 2 S x 2 4 y X Domain Range End Behavior As x f x As x 0 f x intercept Asymptote

Consider the following piecewise defined function f x 2x 4 if x 22 Step 1 of 3 Evaluate this function at x 2 Express your answer as an integer or simplified fraction If the function is undefined at the given value indicate Undefined Answer Keyboard Selecting a radio button will replace the entered answer value s with the radio button value If the radio button is not selected the entered answer is used

Question 9 of 13 Step The distance that a free falling object falls is directly proportional to the square of the time it falls before it hits the ground If an object fell 75 ft in 4 seconds how ld it have fallen by the end of 8 seconds Round your answer to the nearest integer if necessary Answer Keypac Keyboard Shortcu

How many nonzero terms of the Maclaurin series for In 1 x do you need to use to estimate In 1 4 to within 0 01

5 12 x 3 y 48 rotated 30 from its position in the xy plane 40

94 94 Suppose that a 10 and b 3 Compute the sum i 1 i 1 94 26a 206

Consider the function f x sin x 1 cos x a Determine the EXACT x values of the local extrema over the interval 0 21 b Is the function increasing or decreasing at x 3 marks 2 JUSTIFY YOUR JORK EMATIC ALLY

A golf ball is driven into the air at a speed of 86 miles per hour at an angle of 55 from the horizontal Express this velocity in vector form Round your answer to four decimals Answer 6 Points Keyp Keyboard Short

3 Answer 3 Points 3 61 Step 1 of 2 Determine the domain and range for the relation in interval notation 3 XA

B 4 1 4 C 1 3 B D The distance from B to B is 6 and the distance from A to B is 2 What is the scale factor 3 D A

David is trying to solve the following If 24 people have the flu out of 360 people how many would have the flu out of 900 Choose EVERY proportion that David could use to solve this problem 900 360 360 24 24 360 24 360 900 H 900 900

1 point Mac is 5 feet tall and casts a 4 foot 6 inch shadow At the same time a nearby tree casts a 20 foot shadow Which is the closest to the height of the tree 22 feet 18 feet 22 feet 2 inches 18 feet 6 inches

A 3 C B 6 D B 9 C What is the scale factor of the dilation 3 1 3 1 2 D

The following table shows the height at half second intervals of a rock that breaks free from the top of a 290 foot tall cliff and falls without obstruction to the river below Time in seconds 0 0 5 1 0 Step 3 of 3 Which model appears to be more appropriate Answer 1 5 2 0 2 5 3 0 quadratic model Height in feet 290 286 274 254 226 190 146 Keypad Keyboard Shortcuts

Consider a function f x defined as follows f x f 0 to x sin t 2 dt a Determine the derivative of f x with respect to x b Find the second derivative of f x with respect to x c Find the third derivative of f x with respect to x d Compute the value of f n

Use the Cartesian to Polar graphing technique to find the polar graph of r 3 4 cos 0 Show all work to receive full credit Your work should include both a rectangular r vs 0 graph and a polar graph

Step 2 of 2 Use the quadratic formula f x 2x 8x 4 to determine the coordinates of the vertex of the best fitting parabola Write the exact answer Do not round Answer h D Ke Keyboard She

Question L2 The graph of y f x is shown the graph goes through the point 1 1 Provide two different graph transformations that produce the graph of y f x as follows First provide a sequence of transformations of the graph of y log x that produce the graph This sequence should use only horizontal shifts and stretches Second provide a different sequence of transformations that produce the graph Your second sequence of transformations must include a vertical shift or stretch Your grade will be based on how accurately your described transformations reproduce the graph shown 6 2 4 2 0 2 0 2 4 6 8

Tutorial Exercise Sketch the graph of f Then identify the values of c for which lim f x exists X C f x x 5 6 0 8x 4 Step 1 To sketch the graph of f first consider f x x for x 2 by constructing a table of values X x 2 2 x 7 x 7 f x 2 1 1 0 1 1 2

Rolsonut serbe a levisani Find the equation of tangent line to the curve x xy y2 3 at point 1 1

Use the fundamental identities to find the value of the trigonometric function Find cot 8 if csc 8 0 5 and tan 8 0 02 01 10 12 10 O 5

Plot the point with the given polar coordinates S O N 1 2 2 H

Find the magnitude and direction angle for the following vector Give the direction angle as an angle in 0 360 rounded to the nearest tenth 2i 5j O 29 111 8 29 111 8 O 29 68 2 7 291 8

Convert the radian measure to degree measure Use the value of found on a calculator and round answers to two decimal places 57 216 300 150

arlena has started taking photos at amateur dog racing events later offering the photos for sale to the dog owners by email The prices she has charged per photo at ach of her first three events and the corresponding number of photos sold and total revenue raised appear in the table below Price per Photo 52 44 32 400 Treating revenue as a function of the number of photos sold a graph of the three data points is also shown If she uses quadratic regression to fit a curve to the data what number of photos sold and what price per photo will maximize her revenue Revenue 350 300 250 200 150 100 Number of Photos Sold 5 7 10 50 Revenue 260 308 320 Enable Zoom Pan

Consider the following function r x x 6x 5 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 A B

Suppose that y is inversely proportional to the 4th power of x and that y 13 when x 7 What is y when x 3 Round your answer to two decimal places if necessary Answer Keypa Keyboard Short

The safe load L of a wooden beam supported at both ends varies jointly as the width w and the square of the depth d and inversely as the length LA wooden beam 2 in wide 6 in deep and 7 ft long holds up 31969 lb What load would a beam 5 in wide 8 in deep and 13 ft long of the same material support Round your answer to the nearest Integer if necessary Answer Keypad Keyboard Shortcut

Find the indicated sum for each of the following Question S7 5 10 20 S10 54 18 6 S7 24 12 6 Answer

Determine whether the following statements are true or false Prove your answer 1 The product of two irrational numbers is irrational 2 The product of two rational numbers is rational

Find the sum of each series 3 6 12 24 768

32 43 54 to 17 terms 19 14 9 to 23 terms 68 61 54 to 10 terms 13 24 35 156 15 11 7 37 1 6 1 3 2 5 3 the

Select all of the following graphs which represent y as a function of x and is one to one 0 4 32 5 4 3 2 54 3 2 5 4 E t 6 244 50 i 3 321 Na 50 45 S A B N 12 3 N d 0 5 4 3 2 5 4 3 2 O 5 4 3 5 4 3 IN T 2 5 4 10 w 427 3 38 The 23 2 3 4 N p O

At which angle is seco 2 7x 6 5T A 77 4 117 6

12 Determine the minimum of f x 10x 3x x 5 starting at x 3 and using a step size A 5 0 Using region elimination expanding pattern bounding plu

1 Find a simplified expression for cos tan

What is the least common multiple of 15 and 25

20 15 10 5 3 The x intercept of y x X 3 enter the coordinates of the x intercept Solve f x solutions X The y intercept of y x 63 enter the coordinates of the y intercept 3 5 10x Bx 63 is Invalid notation 9 10 3 x 10x Bx 63 is Invalid notation 7 i 35 7 i 35 2 2 0 Find all solutions including complex 15 If there is more

Find the maximum and minimum values of x y subject to the constraint x2 6x y 10y 0

In ARST r 9 5 cm ZT 123 and ZR 40 Find the length of s to the nearest 10th of a centimeter

The graph of a y f x is shown 6 5 4 3 2 1 1 2 3 interval notation 6 5 4 3 2 1 4 5 6 The domain of f x is x The domain of g x 1 2 3 4 5 6 Enter your answer in f x is x Enter your answer in

05 01 5 04 5 05 HC Part A Given sin8 determine three possible angles on the domain 0 5 points Part B Given 8 675 convert the value of 0 to radians and find sec 8 5 points

Find the relative maximum and minimum values f x y x y 12xy Select the correct choice below and if necessary fill in the answer boxes to complete your choice OA The function has a relative maximum value of f x y at x y Simplify your answers Type exact answers Type an ordered pair in the second answer box OB The function has no relative maximum value Select the correct choice below and if necessary fill in the answer boxes to complete your choice O A The function has a relative minimum value of f x y at x y Simplify your answers Type exact answers Type an ordered pair in the second answer box OB The function has no relative minimum value

Part 1 The curves y f x and y g x are shown you may assume and g are polynomials with real coefficients one is the graph of a quadratic and the other is the graph of a cubic and that there are no additional turning points 30 1 Consider the equation f x g x Which of the following are true There is one real solution and two complex solutions There is one real solution and no complex solutions There are three real solutions There is one real solution and one complex solution

Part 1 Suppose Sally want to put a fence around a rectangular field where the width w is two times the length 1 Give an expression for the perimeter of the field in terms of its length 1 perimeter Is the perimeter of the field function of its length O yes O no Explain with one sentence why or why not Part 2 Is the area of the field a function of its length O yes O no Explain with one sentence why or why not

Part 1 Here is the graph of 3 cos 3x the interval TT A 3 cos 3x 1 T 4 B C TT pi or select in the math editor Give the coordinates of point A the y intercept To enter type over Give the coordinates of point B the first x intercept along the positive x axis Give the coordinates of point C the first peak of the graph with positive x value

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The graph of f x is shown it goes through the point 3 5 5 4 3 10 2 1 5 5 10 3 5 2 3 4 5 6 7 8 9 10 Provide two different graph transformations that produce the curve y f x from the curve y log x as follows Q 1 The graph can be obtained from the curve y log x by a horizontal translation followed by a vertical translation Give such a pair horizontal translation by vertical translation by then 2 The graph can be obtained from the curve y log x by a horizontal stretch followed by a horizontal translation Give such a pair horizontal stretch by factor then 2

Use the given triangle to evaluate the trigonometric expression 13 12 cos

4 points Decide from the graph whether or not the integral edx might converge If the integral migh 8 0 converge find out whether or not it does and if so the limit to which it converges to the nearest thousandth Work