What is the extreme f(x)=4x^2(x-6) ?

The extreme f(x)=4x^2(x-6) is Maximum(0,0),Minimum(4,-128)

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extreme f(x)=4x^2(x-6)

extreme points

f (x) = 4 x^{2} (x - 6)

Maximum (0, 0), Minimum (4, - 128)

Solution steps

f^{'} (x) = 4 (3 x^{2} - 12 x)

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = 0

into

4 x^{2} (x - 6) : 0

Maximum (0, 0)

Plug

x = 4

into

4 x^{2} (x - 6) : - 128

Minimum (4, - 128)

Maximum (0, 0), Minimum (4, - 128)

What is the extreme f(x)=4x^2(x-6) ?
The extreme f(x)=4x^2(x-6) is Maximum(0,0),Minimum(4,-128)