Question

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem.

f(x) = x^3 − x^2 − 2x + 5, [0, 2]

Answer 1

Derivative is 3x^2-2x-2

F(2) = 5
F(0) = 5
F(2)=F(0) = 0

3x^2-2x-2=0

Answer 2

satisfies the hypotheses because any polynomial is continuous and differentiable
you last job is to set
\[3x^2-2x-2=0\] and solve for \(x\)

Answer 3

but i am confused, because you wrote \(f(2)=5\) and later wrote \(f(2)=0\)
it can't be both