Question

Help with calculus problem...

Answer 1

a) Use the product rule:

\(y'=2[f(x)g'(x)+g(x)f'(x)]\)

\(y'(4)=2[f(4)g'(4)+g(4)f'(4)]\)

Answer 2

From her, plug in the numbers from the question

Answer 3

So a is 108

Answer 4

yes

Answer 5

Quotient rule with part b?

Answer 6

right

Answer 7

That's 66/36 or 11/6

Answer 8

yep

Answer 9

Part c has been giving me some troube

Answer 10

use the chain rule to find the slope of the tangent line.

2(3 f(x)) f'(x) or 6 f(4) f'(4)

Answer 11

so the slope is 108

Answer 12

Then find the y-coordinate at x = 4

3(f(4))² = 3(6)² = 108

So in point-slope form the equation of the tangent line is

y - 108 = 108(x - 4)

Answer 13

I see...thanks!

Answer 14

yw