Question

Decide whether Rolle's theorem can be applied to f(x) = x^2 + 5 on the interval [0, 3]. If Rolle's theorem can be applied, find all value(s) of c in the interval such that f '(c) = 0.

Answer 1

1) Differentiate, and set, f'(x)=0
Then, the x-solutions that satisfy this equation (provided x=[0,3]), are your answers.

Answer 2

But, you can't right off, though.
The slope of the secant isn't zero.