Question

Given that h(x)=x^2g(x) and g(3)=5 and g'(3)=7 find h'(3)

Answer 1

You can use the product rule.
h'(x) = f(x)g'(x) + g(x)f'(x)
where in this problem f(x) = x²

Answer 2

so f(x)=x^2 and f'(x)=2x

Answer 3

right

Answer 4

then evaluate them both at 3

Answer 5

what about g(x) and g'(x)?

Answer 6

well they're asking for h'(3), so you don't need g(x) and g'(x) since they gave you the values at 3.

Answer 7

so how would you use the product rule?

Answer 8

Above is the product rule generally. Specifically at x = 3.

\[h'(3) = f(3)g'(3) + g(3)f'(3)\]

Answer 9

g(3) and g'(3) are given.
f(3) and f'(3) are found by evaluating x² and 2x at 3 respectively

Answer 10

oh is it h'(3)=9*7+5*6

Answer 11

f(3) = 3² = 9
f'(3) = 2(3) = 6

Answer 12

yep exactly

Answer 13

so the answer is 93

Answer 14

thanks for your help peachpi

Answer 15

yes that's right. You're welcome