Can you please help me? I try very hard but I don’t understand how to do

Question

Given the function f (x) = 2x^3 + 24x^2 + 72x, determine all intervals on which f’ is increasing.

Thank you for the answer.

Answer 1

If you want f'(x) to increase, then f''(x) must be positive
f(x) = 2x^3 + 24x^2 + 72x
f'(x) = 6x^2 + 48x + 72
f''(x) = 12x + 48
so you want 12x + 48 > 0
12x > -48
x > -4

The question could have been asked:
For what values of x is f(x) concave upwards, or opens upwards (holds water)
Look at the original graph, notice you would have a point of inflection when x = -4
I would be concave upwards, (holds water) for x > -4, have a point of inflection at
x = 4 and concave downwards for x < -4

Answer 2

Thank you soooo much.