Suppose the derivative of f exists, and assume that f(5)=3, and f′(5)=5. Let g(x)=x^2f(x), and h(x)=f(x)/x−4.

a) g′(5)=______________
Find the equation of the tangent line to g(x) at x=5.
y=_____________

b) h′(5)=______________
Find the equation of the tangent line to h(x) at x=5.
y=__________________

Question

Suppose the derivative of f exists, and assume that f(5)=3, and f′(5)=5. Let g(x)=x^2f(x), and h(x)=f(x)/x−4.

a) g′(5)=______________
Find the equation of the tangent line to g(x) at x=5.
y=_____________

b) h′(5)=______________
Find the equation of the tangent line to h(x) at x=5.
y=__________________

anonymous · Answer

I know h'(5)= 2 but i'm stumped on the remaining parts

anonymous · Answer

g'(x) = 2xf(x) + x^2f'(x)
can you do it now?

anonymous · Answer

is  g′(5) = 155 ?

anonymous · Answer

yes

anonymous · Answer

@Coolsector oh i did'nt see ur post

anonymous · Answer

that's the right way

anonymous · Answer

why is g'(x) = 2xf(x) + x^2f'(x)? I understand the first part but I dont know where the second part of the equation came in

anonymous · Answer

using the product rule :

g(x) = x^2 * f(x)

g'(x) = (x^2)' * f(x) + (x^2) * f'(x)

anonymous · Answer

in general : (uv)' = u'v + v'u

anonymous · Answer

oh wow I dont know why I didnt see that. Thank you!! :)

anonymous · Answer

yw