What is the extreme f(x)=4x^3-24x^2+36x ?

The extreme f(x)=4x^3-24x^2+36x is Maximum(1,16),Minimum(3,0)

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extreme f(x)=4x^3-24x^2+36x

extreme points

f (x) = 4 x^{3} - 24 x^{2} + 36 x

Maximum (1, 16), Minimum (3, 0)

Solution steps

f^{'} (x) = 12 x^{2} - 48 x + 36

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 1

into

4 x^{3} - 24 x^{2} + 36 x : 16

Maximum (1, 16)

Plug

x = 3

into

4 x^{3} - 24 x^{2} + 36 x : 0

Minimum (3, 0)

Maximum (1, 16), Minimum (3, 0)

What is the extreme f(x)=4x^3-24x^2+36x ?
The extreme f(x)=4x^3-24x^2+36x is Maximum(1,16),Minimum(3,0)