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

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.