What is the extreme f(x)=324x-72x^2+4x^3 ?

The extreme f(x)=324x-72x^2+4x^3 is Maximum(3,432),Minimum(9,0)

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extreme f(x)=324x-72x^2+4x^3

extreme points

f (x) = 324 x - 72 x^{2} + 4 x^{3}

Maximum (3, 432), Minimum (9, 0)

Solution steps

f^{'} (x) = 324 - 144 x + 12 x^{2}

Find intervals:

Increasing

: - \infty < x < 3,

Decreasing

: 3 < x < 9,

Increasing

: 9 < x < \infty

Plug

x = 3

into

324 x - 72 x^{2} + 4 x^{3} : 432

Maximum (3, 432)

Plug

x = 9

into

324 x - 72 x^{2} + 4 x^{3} : 0

Minimum (9, 0)

Maximum (3, 432), Minimum (9, 0)

What is the extreme f(x)=324x-72x^2+4x^3 ?
The extreme f(x)=324x-72x^2+4x^3 is Maximum(3,432),Minimum(9,0)