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

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

ganeshie8 · Answer

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

ganeshie8 · Answer

next, find f'(x)

dumbcow · Answer

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