What is the extreme f(x)=2x^3-24x^2+72x ?

The extreme f(x)=2x^3-24x^2+72x is Maximum(2,64),Minimum(6,0)

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extreme f(x)=2x^3-24x^2+72x

extreme points

f (x) = 2 x^{3} - 24 x^{2} + 72 x

Maximum (2, 64), Minimum (6, 0)

Solution steps

f^{'} (x) = 6 x^{2} - 48 x + 72

Find intervals:

Increasing

: - \infty < x < 2,

Decreasing

: 2 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = 2

into

2 x^{3} - 24 x^{2} + 72 x : 64

Maximum (2, 64)

Plug

x = 6

into

2 x^{3} - 24 x^{2} + 72 x : 0

Minimum (6, 0)

Maximum (2, 64), Minimum (6, 0)

What is the extreme f(x)=2x^3-24x^2+72x ?
The extreme f(x)=2x^3-24x^2+72x is Maximum(2,64),Minimum(6,0)