The absolute extreme values of the function are (-3, 32) and (1, 0)
How to determine the absolute extreme values of the function
From the question, we have the following parameters that can be used in our computation:
x³ + 3x² - 9x + 5
Differentiate the function
So, we have
3x² + 6x - 9
Set to 0
3x² + 6x - 9 = 0
This gives
x² + 2x - 3 = 0
When evaluated, we have
x = -3 and x = 1
Recall that
x³ + 3x² - 9x + 5
So, we have
(-3)³ + 3(-3)² - 9(-3) + 5 = 32
(1)³ + 3(1)² - 9(1) + 5 = 0
Hence, the absolute exterem values of the function are (-3, 32) and (1, 0)