Analyzing functions max and min

Question

Find the x-coordinate of the point(s) of inflection on the graph of y = x³ - 12x² - 5

Choices:

1. x = -2
2. x = 4
3. x = 2
4. x = 12

Answer 1

The function is a cubic function, so it will have one point of inflection which can be found by taking the second derivative and setting it equal to zero.

y = x³ - 12x² - 5

y' = 3x² - 24x

y" = 6x - 24

6x - 24 = 0

6x = 24

x = 4