Question

Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = x3 + x − 3, [0, 2]

Answer 1

Short answer: Yes

The two hypotheses are
1. f(x) is continuous on the interval [0, 2].
This hypothesis is satisfied. A polynomial function is continuous everywhere.

2. f(x) is differentiable on the interval (0, 2).
This hypothesis is satisied. A polynomial function is differentiable everywhere.