Need help of max and min calculus, thank you

Question

What are the critical values on the graph of y = x³ - 12x + 1?

Options:

1. x = -2, 0, 2
2. x = -2, 2
3. x = -4, 4
4. x = -3.42, 0, 3.42

Answer 1

To find the critical points, take the derivative and set it equal to zero. To take the derivative of :

y = x³ - 12x + 1 we use the power rule on each piece so it becomes:

y' = 3x² - 12

Setting that equal to zero, we get:

3x² - 12 = 0

3x² = 12

x² = 4

x = ± 2 (which is answer #2)

Please note that I have an issue with the question. The x values are typically called critical points and the associated function values at those critical points are typically called critical values. But the answers all say "x = " so, I guess it's fine. It's just that if someone asked me what the critical values were, I would find the critical points then plug them into the function to find the critical values which are 17 (when x = -2) and -15 (when x = 2)