Working the Chain Rule

Question

I am again trying to help my daughter with her college homework that is over my head. Any help for the following problem is appreciated.

Find the equation of the tangent line to the graph of y(x)= 12(x-(1/x)^4 at x=2

I am not sure if I am showing her the right way of solving this.

Answer 1

Equation for tangent line will be y - f(2) = f'(2)(x-2) where (2,f(2)) is the coordinate where we are evaluating the derivative. The equation is a line in point-slope form with the derivative as the slope.

You need f(2) and f'(2) Your function is missing a parenthesis. I'm going to assume y = 12(x - (1/x)⁴)

f(2) = 12(2 - 1/16) = 45/4

f'(x) = 12 - 12(-4x^-5) = 12 + 48/x⁵ f'(2) = 12 + 48/32 = 27/2

y-45/4 = (27/2)(x-2)

Please consider a tutor. Take care.