# Find all numbers $c$ that satisfy the conclusion of the Mean Value Theorem for the function $f(x) = x^3 −1$ on the interval $[−1,1]$.

so as the title says Find all numbers $$c$$ that satisfies the conclusion of the Mean Value Theorem for the function $$f(x) = x^3 −1$$ on the interval $$[−1,1]$$.

i tried to solve it and it satisfy the conclusion and there should be a $$C$$, but when i solved it there is no $$c$$ because $$x^2=-\frac13$$ which is impossible and there no $$c$$ here, it ok?

• What does the $c$ in your problem mean? Dec 9 '19 at 19:18

We want to find all numbers $$c \in \langle -1,1\rangle$$ such that $$f(1) - f(-1) = f'(c)(1-(-1))$$
or $$2 = 3c^2 \cdot 2$$
We get $$c^2 = \frac13 \implies c = \pm \frac1{\sqrt3}$$