Question

given g(2)=3, g'(2)=-2, h(2)=-1, h'(2)=4
a) if f(x)=2g(x)+h(x), find f'(2)
b) if f(x)=4-h(x), find f'(2)
c) if f(x)=g(x)/h(x), find f'(2)
d) if f(x)=g(x)h(x), find f'(2)

Answer 1

for each,
first find \(f'(x)\), then plugin \(x=2\)

Answer 2

I am still confused, can you walk me through a and I'll see if I can do the rest on my own?

Answer 3

@ganeshie8

Answer 4

\[\large\rm f(x)=2g(x)+h(x)\]The derivative of f(x), with respect to x, is f'(x), yes?

Answer 5

Likewise, the derivative of g(x), with respect to x, is g'(x).
There is nothing fancy going on in this first problem.
No product rule, no composition, nothing special :)\[\large\rm f'(x)=2g'(x)+h'(x)\]

Answer 6

oh, and then you would plug in the given values of g'(x) and h'(x)?

Answer 7

\[\large\rm f'(\color{orangered}{x})=2g'(\color{orangered}{x})+h'(\color{orangered}{x})\]They want us to evaluate this at x=2,\[\large\rm f'(\color{orangered}{2})=2g'(\color{orangered}{2})+h'(\color{orangered}{2})\]And yes, use that chart at the top to plug in the missing pieces on the right :)

Answer 8

great! so it would be 2(-2)+4, so 0

Answer 9

Good!