QuestionThe function $f(x)=2 x^{3}-33 x^{2}+168 x-10$ has two critical numbers.
Give the two critical numbers as a commaseparated list. $$x=$$ $\square$

Studdy Solution
Verify the solutions by substituting back into the derivative to ensure they make it zero:
For $x = 4$: $$f'(4) = 6(4)^2 - 66(4) + 168 = 0$$
For $x = 7$: $$f'(7) = 6(7)^2 - 66(7) + 168 = 0$$
Both solutions satisfy the equation.
The two critical numbers are:
$$\boxed{4, 7}$$