Question

Determine if the function
f(x) = 1 + x − x^3
satisfies the hypotheses of the Mean Value
Theorem (MVT) on the interval [−2, 1].
If it does, find all possible values of c

Answer 1

a polynomial is continuous and differentiable everywhere,
given function is a polynomial
so it satisfies the hypothesis of MVT

Answer 2

next, find f'(x)

Answer 3

\[f'(c) = \frac{f(1) -f(-2)}{1-(-2)}\]
\[f'(c) = -2\]
\[1-3c^{2} = -2\]
\[c = \pm 1\]