Find the Derivative Functions and Values?

Question

(x-1)^2 +1; F'(-1) F'(0)

Answer 1

What is f(x)?
Is it (x-1)^2+1 ???
Then f'(x) = 2(x-1)*1 + 0 = 2(x-1)
So f'(-1) = 2(-1-1) = 2(-2) = -4
And f'(0) = 2(0-1) = 2(-1) = -2
You find the derivative using the chain rule. Outer function first, then inner function. You also use the power rule in the process.

Answer 2

Assuming that

F(x) = (x - 1)^2

Then

F'(x) = 2(x - 1) = 2x - 2, so
F'(-1) = 2(-1) - 2 = -2 - 2 = -4

F'(0) = 2(0 - 1) = 2(-1) = -2