Question

PLEASE HELP !

The function
f(x) = 2x ^ 3 - 24x ^ 2 + 72x + 6 has one local minimum and one local maximum. Use a graph of the function to estimate these local extrema.
This function has a local minimum at x =
With output value:
and a local maximum at x =
with output value:

Answer 1

f(x) = 2x³ - 24x² + 72x + 6

f'(x) = 6x² - 48x + 72

x² - 8x + 12 = 0

(x - 2)(x - 6) = 0

x = 2, 6

The function has a local minimum at x = 6 with output value f(6) = 6.

The function has a local maximum at x = 2 with output value f(2) = 70.