Question

Help Please !!!
Find h′(2) given that f(2) = −1, f′(2) = 4, g(2) = 1, and g′(2) = −5. solve each one
a. h(x) = 5f(x) + 2g(x).
b. h(x) = f(x)g(x).
c. h(x) = f(x)/g(x).
d. h(x) = ln f(x).

Answer 1

please help someone

Answer 2

@hooverst
We'll solve each option
a)h(x)=5f(x)+2g(x)
Let's differentiate this
\[h'(x)=5f'(x)+2g'(x)\]
we want to find h'(2) so put x=2
\[h'(2)=5f'(2)+2g'(2)\]
Can you solve now?

Answer 3

@ash2326 good :)

Answer 4

yes

Answer 5

plug x as 2 in given expression as\[h(2)=5f(2)+2g(2)\]\[h(2)=5(-1)+2(1)\]\[h(2)=-5+2=-3\]

Answer 6

Can you differentiate b?
\[f(x)=h(x)\times g(x)\]

Answer 7

&\[h(2)=5(2)+2(-5)\]\[h(2)=10+(-10)=0\]

Answer 8

ok got it.

Answer 9

@hooverst Did you try the third option?

Answer 10

I'm working on it now I would divide right?

Answer 11

the one above how is that 5(2) instead of 4(2)

Answer 12

\[h'(x)=f'(x)\times g(x)+f(x)\times g'(x)\]
x=2
\[h'(2)=f'(2)\times g(2)+f(2)\times g'(2)\]
\[h'(2)=4\times 1+(-1\times -5)=4+5\]

Answer 13

@hooverst do you know the quotient rule of division?

Answer 14

yes

Answer 15

would the anserw be 0 for c ?

Answer 16

I'm not sure if I did it right.