Question

Suppose that f(2)=-3, g(2)=4, f'(2)=-2, and g'(2)=7. Find h'(2).
a. h(x)=5f(x)-4g(x)
b. h(x)=f(x)g(x)
c. h(x)=f(x)/g(x)
d. h(x)=g(x)/1+f(x)

Answer 1

Do you know how to differentiate?

Answer 2

If we have \[
h(x) = 5f(x)-4g(x)
\]We differentiate both sides and get \[
h'(x) = 5f'(x)-4g'(x)
\]

Answer 3

Yes, my professor talked about it this morning. I'm just getting confused with the overall process.

Answer 4

Okay, can you do the first one?

Where are you stuck?

Answer 5

Would you use the product rule for the first one?

Answer 6

First one? Doesn't have any function multiplication though...

Answer 7

I did the first one.

Answer 8

So that's as far as you'd go on the first one?

Answer 9

I guess I get confused on where I should stop. As well as which rule applies to which problem

Answer 10

Well, then you let \(x=2\) and it all sorts itself out.

Answer 11

\[
h'(2)=5f′(2)−4g′(2)
\]

Answer 12

Then you can just substitute.

Answer 13

Okay, that makes sense.

Answer 14

Thanks!