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

The extreme f(x)=24x^3-3x^4 is Saddle(0,0),Maximum(6,1296)

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extreme f(x)=24x^3-3x^4

extreme

Saddle (0, 0), Maximum (6, 1296)

Solution steps

f^{'} (x) = 72 x^{2} - 12 x^{3}

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 6,

Decreasing

: 6 < x < \infty

Plug

x = 0

into

24 x^{3} - 3 x^{4} : 0

Saddle (0, 0)

Plug

x = 6

into

24 x^{3} - 3 x^{4} : 1296

Maximum (6, 1296)

Saddle (0, 0), Maximum (6, 1296)

What is the extreme f(x)=24x^3-3x^4 ?
The extreme f(x)=24x^3-3x^4 is Saddle(0,0),Maximum(6,1296)