Question

Linear approximation:

Consider the curve defined by
-8x^2 + 5xy + y^3 = -149
a. find dy/dx
b. write an equation for the tangent line to the curve at the point (4,-1)
c. There is a number k so that the point (4.2,k) is on the curve. Using the tangent line found in part (b), approximate the value of k
d. Write an equation that can be solved to find the actual value of k so that the point (4.2,k) is on the curve
e. Solve the equation found in part (d) for the value of k

I have already figured out:
a. dy/dx=16x-5y/5x +3y^2
b. y+1=3(x-4)

I am just having trouble solving c, d, and e

I would really appreciate any help I can get! Thank you!!

Answer 1

(c),(d) just plug in 4.2 for x and solve for y. That will be the value for k.


Since (d) will be a cubic in y, it might take a graphical solution.