What is the relative maximum and minimum of f(x)=x^3-12x+2?

Question

Using the first derivative test to determine the relative maximun and minimum of problem. Thank you.

Answer 1

f `(x ) = 3x² - 12 = 3(x² - 4) = 3(x - 2).(x + 2)
f "(x) = 6x
For turning points , f `(x) = 0
x = 2 and x = - 2 for turning points
f " (2) is positive (MIN turning point when x = 2)
f "(-2) is negative (MAX turning point when x = - 2)
f(2) = 8 - 24 + 2 = - 14
f(- 2) = - 8 + 24 + 2 = 18
(2,-14) is a MINIMUM turning point
(-2,18) is a MAXIMUM turning point.

Answer 2

maximun is 4

mimimum is 2