Question: Let y (x 2 + 4) = 8 a. Use implicit differentiation to find dy/dx. b. Find equations of all lines tangent to the curve

Let y (x2 + 4) = 8

a. Use implicit differentiation to find dy/dx.

b. Find equations of all lines tangent to the curve y(x2 + 4) = 8 when y = 1.

c. Solve the equation y(x2 + 4) = 8 for y to find an explicit expression for y and then calculate dy/dx.

d. Verify that the results of parts (a) and (c) are consistent.

y, У(? + 4) 3 8 -2 -4 4 х

y, (? + 4) 3 8 -2 -4 4

Step by Step Solution

★★★★★

3.37 Rating (172 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a y2x x 2 4y 0 so y 2xyx 2 4 b At y 1 we have x 2 4 8 so ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Calculus Early Transcendentals Questions!

Q:

The Power Rule can be proved using implicit differentiation for the case where n is a rational number, n = p/q, and y = f (x) = x n is assumed beforehand to be a differentiable function. If y = x p/q...

Q:

A trough in the shape of a half cylinder has length 5 m and radius 1 m. The trough is full of water when a valve is opened, and water flows out of the bottom of the trough at a rate of 1.5 m 3 /hr...

Q:

A revolving searchlight, which is 100 m from the nearest point on a straight highway, casts a horizontal beam along a highway (see figure). The beam leaves the spotlight at an angle of /16 rad and...

Q:

ii. lim f (x) 4. (10 points) Use implicit differentiation to find the equation(s) of the tangent line(s) to the graph of ya - xy - 6 =0 at the point(s) with the given value of x =1. 5. (10 points)...

Q:

Are there any easy ways to solve these?

Q:

Please help with these calculus questions 7. [-/1 Points] DETAILS LARSONET5 3.5.040. Find the slope of the tangent line to the graph at the given point. x3 + y3 - 6xy = 0, (4/3, 8/3) X Your answer...

Q:

Could you help me with my calc work? If f(x) + x [f(x)]3 = 10 and f(1) = 2, find f '(1). f '(1) =Use implicit differentiation to find an equation of the tangent line to the curve at the given point....

Q:

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. 25 (x2 + 12) = (x2+ 12 - 9x)2 (0, 5) (Limacon)Use implicit differentiation to find an equation of...

Q:

6. Given f(x) = v(5x3 - 5x) , find the derivative of f and the values of x where the tangent line is horizontal. (5 pts) 7. The total cost (in hundreds of dollars) of producing x cameras per week is...

Q:

6. [-/1 Points] DETAILS 0/100 Submissions Used If ((x) + x2[f(x)]* = 10 and /(1) = 2, find f '(1). F '(1) = 7. [-/1 Points] DETAILS 0/100 Submissions Used Use implicit differentiation to find an...

Q:

THE ETHICAL DIMENSION Is the courts decision in this case fair to employers? Why or why not? Josephine Mora was sixty-two years old when she was fired from her job as a fund-raiser for Jackson...

Q:

Use superposition to find vo in the circuit of Fig. 4.81. Figure 4.81 For Prob.4.13 4 A 8 12 V 2 A 10

Q:

58. At Break-even point the organisation will have: (a) Maximum profit, ( ) (b) No loss and no gain, ( c) Maximum loss, ( ) ( d) Moderate profit.

Q:

The daily weather in Fayettville, Arkansas, can be cloudy (C), sunny (S), rainy (R), or windy (W). Records over the past 90 days are CCSWRRWSSCCCRCSSWRCRRRR...

Q:

Evaluate the integral. 10 + 10*) dx Jo

Q:

Evaluate the integral. 'T/4 sece tan0 do

Q:

Evaluate the integral. (7/4 1 + cos0 de cos'e

Q:

Assume the following information: Assume the equivalent units of production for materials and conversion are 5,200 units and 5,000 units, respectively, using the weighted-average method. If 4,630...

Q:

calculate the missing numbers from the yellow cells. Dooley, Inc., has outstanding $100 million bonds that pay an annual coupon rate of interest of 10.5 percent. Par value of each bond is $1,000. The...

Q:

The spot price of gold is currently $1,694/oz, while the 4 -month forward price is $1,729/oz. If gold has no convenience yield, what is the implied repo rate? Express the implied repo rate in % with...