A function $f(x)$ and interval $[a, b]$ are given. Check if the Mean Value Theorem can be applied to $f$ on $[a, b]$. If so, find all values $c$ in $[a, b]$ guaranteed by the Mean Value Theorem.
$f(x) = 2x^3 - 9x^2 - 24x + 6$ on $[-6, 9]$
c =
(Separate multiple answers by commas.)
Note: You may need to use the quadratic formula for this problem. Recall that the solutions to $ax^2 + bx + c = 0$ are $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. If the Mean Value Theorem does not apply, enter DNE for the c value.