Question

Verify that f,defined by f(x)=x^3+4x+1 on [1,5], satisfies Lagrange's mean value theorem.?

Answer 1

Please see below.

Explanation:

`f` is a polynomial, so `f` is continuous on `[1,5]`

`f'(x) = 3x^2+4` exists for all `x` in `(1,5)` so `f` is differentiable on `(1,5)`

Therefore, `f` "satisfies the Mean Value Theorem".