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. (Enter your answers as a comma-separated list.)

f(x) = 5 − 6x + 3x2, [0, 2]

can someone please explain this. thanks

Answer 1

f(0) = 5
f(2) = 5
so, that is ok.

f(x) is continuous
since f is a polynomial, it is differentiable

So, we want c such that f'(c) = 0
6c-6 = 0
c = 1

ok, since 1 is in [0,2].