Question

Supposed f(4) = 2, f(2) = 3, f'(4) = -1 and f'(2) = 4. Let G(x) = (f(x))^2. Evaluate G'(2). Final answer is a single number

Answer 1

This is where you want to use the chain rule. By the chain rule\[{d \over dx} \;\; (f(x))^2=2f(x)f'(x)\]If you plug in 2 for \(x\), you find\[G'(2)=2f(2)f'(2)=2*3*4=24\]

Answer 2

very helpful! thank you!

Answer 3

You're welcome.