Question

How do you show that `f(x)=6x^2 - 24x + 22` satisfies the hypotheses of Rolle's theorem on [0,4]?

Answer 1

Use the fact that this function is a polynomial.

Explanation:

`f(x)=6x^2 - 24x + 22` is continuous on `[0,4]` because it is a polynomial and polynomials are continuous at every real number.

`f` is differentiable on `(0,4)` because it is a polynomial so its derivative is a polynomial which is defined for all real numbers, so of course the derivative is defined on `(0,4)`