Differentiation Questions and Answers

In Problems 50 53 find y using implicit differentiation 50 sec y xy 1

ous at r a Illustrate each case with a picture 9 How can a function f x fail to be differentiable at a number 1 illustrate each case with a picture 10 Give the accurate definition of a concave upward and a each case with CORS Explain a Explain all cases and

Use implicit differentiation to find dy dx and d y dx x3 5 y3 5 8 O dy y2 5 d2y x2 5 dx2 O F O dy y2 5 d2y x2 5 dx2 y2 5 d2y x2 5 dx2 dy x2 5 d y dx y2 5 dx2 2y1 5 2x T 5x7 5 3 5 2x3 5 273 5 5x7 5 1 5 2x3 5 2y3 5 5x7 5 1 5 2x3 5 2y3 5 5x1 5 7 5

Boyle s law states that the volume of a gas varies inversely with applied pressure Suppose the pressure on 60 cubic meters of gas is raised from 1 atmosphere to 3 atmospheres What new volume does the gas occupy cubic meters

Suppose that a y 82 dy 1 Use the method of implicit differentiation to find da dy dx x3 2 Find the equation of the tangent line at the point x y 3 1 The equation is X 27x80

The curvature of the helix r t a cost i a sin t j bt k a b20 is x The largest value x can have for a given value of b is a a What is the largest value x can have for a given value of b www

Find T N and x for the plane curve r t 4cost 4t sin t i 4sin t 4t cos t j t 0

L et et dt Find an equation of the tangent line to the curve y x at the point with x coordinate 3 Let F x

Evaluate the integral 64 100 x 5 6 d dx

15 Find an equation of the tangent line to the graph of the function f x x 3x 3 3 3 at the point a y 6 b y 3x 6 c y 9x d y 3x e y 9x 24

14 Find the derivative of the function a b c d le 5 2 5x 2 5 2 5x 2 5x 5x 2 5 x 5x 2 f x f x f x f x 5 5x 2 f x 5x 2

Find the derivative of the function 5 3 y In 5x6 7x 5

Find the derivative of the given function y 2x 6x e 8x 7

Find the derivative of y with respect to x for y 2 dv

Find the derivative of the given function 575 41 5e 4x y y

Find the derivative of the given function y In 26x 4x y 0

Find the derivative of the given function y x e 5x y

Estimate the area of the region bounded by the x axis and the graph of y sin x from x 0 to x 3 using six rectangles and using right endpoints Draw the region and show your six rectangles Write your solution on paper and upload an image of a PDF file of your solution

The tangent line to a smooth curve r t f t l g t h t k at t to is the line that passes through the point to 9 to h t parallel to v to the curve s velocity vector at to User to and r to to find parametric equations for the line that is tangent to the given curve at the given parameter value t to r t cos t i 3 sin t j 3 k o 0 Find the standard parametrization for the tangent line OA x 1 y 3t z 3 9t OB x 1 y 2t 3 z 3 c x 0 y 3t z 3 9t D x 0 y 2t 3 z 3 CIES

ear total active iPhones in US in millions of units 8 17 24 40 51 72 88 101 114 125 127 131 138 141 149 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 total active iPhones in US in millions of units vs year 7 17 11 8x 2 12x 2 0 0578x 3 total active iPhones in US in millions of units 150 100 50 0 8 10 12 14 year 16 18 20 22

Given the table of values below find the average rate of change of the function f x on the interval 5 13 4 9 70 162 X f x 5 94 6 102 7 123 8 141 10 195 11 199 12 232 13 238 14 251

Augustus bor 2 In the subtraction below a b and c are digits and a is less than 6 What is the value of e ba ab cfi

Find the derivative f x 8 2x 3 C

Differentiate the function y 38 1 4x 3 5 11

37 Aidan and his sister Ella are having a race Aidan runs at a rate of 10 feet at a rate of 6 feet per second Since Ella is younger Aidan is letting her begin 30 feet ahead of second Ella runs per the starting line Let y represent the distance from the starting line and x represent the time elapsed in seconds Write an equation to model the distance Aidan traveled Write an equation to model the distance Ella traveled

Determine the infinite limit O a 8 O 00 18 x 2 lim X 7 X 7

Express the lengths a and b in the figure in terms of 0 a 5 11 0 18 b a i

1 x If x 0 2x 1 If x 0 Let f x Evaluate f 7 and 2 f 7 f 2 If you have had difficulty with these problems you should look at Sections 1 1 1 3 of yo

Rewrite by completing the square 2x 4x 11 If you have had difficulty with this problem you may wish to cons

Expand and simplify 2 x 6 3 4x 5 If you have had difficulty with this problem you may wish t

Answering calcPad Questions VebAssign calcPad questions are displayed with a rectangular answer box similar to answer boxes used for other question types but when you click a calcPad enabled answer box the calcPad pa pens allowing you to answer the question with a correctly formatted mathematical expression This exercise requires you to enter a mathematical expression Your answer should be To enter this answer 1 Click the answer box to open the calcPad palette VO 2 Click in the palette

mathematics expressions are case sensitive 3x is not the same as 3X WebAssign follows these rules his exercise requires you to enter a mathematical expression Enter D P To enter this answer 1 Click the answer box to open the calcPad palette 2 Type D p pi 3 Notice that the word pi has automatically changed to the symbol 4 Submit your answer

Find the first five terms ao a1 02 03 04 in the series solution at z 0 of the initi value problem IVP x 1 y xy y 0 y 0 0 y 0 1

Find the value of f 25 if f t 8 t SUOR 3 t

Determine the equation of the line passing through the points 1 1 and 1 7 Write the line in standard form Ax By C

Let f x y 5x xy e evaluate f 4 3 f 3 0 2 Let g x y 0 25x 3x y find the followin partial derivatives A gx B gy

3 Let z 800 62xy 15y evaluate dz A 2 1 dx B z 2 3 4 Let R x y 0 1x y4 5x 6y find the secon partial derivatives A B 8 R dy a R a ar oxdy dx dy

THE nd the equation of the linear function whose graph is given here Use the letter X ultiplication symbol 654321 7 6 5 4 3 2 1 21 4567 LLLL 1 2 3 4 5 6 7 Son 1

of the given function f x 4x5 2x5 x 5x 5

Find the equation of the line passing through the points 7 7 and 7 5 Your answer should take the form x aor y a whichever is appropriate

Alden Company s monthly data for the past year follow Management wants to use these data to predict future variable and fixed costs Month Units Sold 320 000 160 000 2 Units Income 280 000 200 000 300 000 200 000 Total Cost 160 000 100 000 220 000 100 000 230 000 120 000 Contribution margin Fixed costs Income Predictions 220 000 0 Month 7 8 b 9 2 Predict future total costs when sales volume is a 220 000 units and b 240 000 units 10 11 12 240 000 Units Sold 340 000 280 000 80 000 0 160 000 100 000 110 000 Total Cost 220 000 160 000 64 000 140 000 100 000 80 000

From the table below we can conclude that the function f has a local maximum at x f x 3 6

Rewrite the integral in terms of k dv Step 3 H K V Let u xe Substitute the value of k du 1 C 1 N 7 7x 1 2 7 k dk xe7x Differentiate u with respect to x Jx dx xe7x e dk 7 1

64 64 1 1 sin x Step 4 Recall the Pythagorean identities which state that sin u cos u 1 1 tan u sec u 1 cot2 u csc u Use the appropriate Pythagorean identity Therefore the expression simplifies to

Find the derivative of the following function dr ds r 11 1 3 4s 7 2 3s

Find the derivative f x x 2x 4 8x 16 A f x 1 33x 2 4x 1 2 8 OB f x 3x 2 4x 1 2 8 OC f x 3x 2 2x 1 2 8 2x 1 2 OD f x 1 33x 1 33x1 2 8

Find the derivative of the function y 10x 10x 2x dy

Assume that a demand equation is given by x 7000 100p Find the marginal revenue for the given production levels values of x Hint Solve the demand equation for p and use R x xp a 2000 units b 3500 units c 4500 units a Choose and fill in the correct response for x 2000 OA The marginal revenue at 2000 units is per production level OB The marginal revenue at units is 2000 production levels per 1 units is 2000 per production level OC The marginal revenue at OD The marginal revenue at 2000 units is production levels per 1 b Choose and fill in the correct response for x 3500 OA The marginal revenue at OB The marginal revenue at 3500 units is OC The marginal revenue at units is 3500 OD The marginal revenue at 3500 units is c Choose and fill in the correct response for x 4500 units is 3500 per production level production levels per 1 production levels per 1 per production level OA The marginal revenue at 4500 units is per production level GELER

Find the following 7 x f 4 if f x x O A OB O C OD 3 7 60 16 3 16 11 16 11 16

Find the following f 2 if f x x4 8x 2x 2 OA 64 OB 62 OC 32 OD 34