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

The extreme f(x)=-x^3(x-3) is Saddle(0,0),Maximum(9/4 , 2187/256)

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

extreme

Saddle (0, 0), Maximum (\frac{9}{4}, \frac{2187}{256})

Solution steps

f^{'} (x) = - 4 x^{3} + 9 x^{2}

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{9}{4},

Decreasing

: \frac{9}{4} < x < \infty

Plug

x = 0

into

- x^{3} (x - 3) : 0

Saddle (0, 0)

Plug

x = \frac{9}{4}

into

- x^{3} (x - 3) : \frac{2187}{256}

Maximum (\frac{9}{4}, \frac{2187}{256})

Saddle (0, 0), Maximum (\frac{9}{4}, \frac{2187}{256})

What is the extreme f(x)=-x^3(x-3) ?
The extreme f(x)=-x^3(x-3) is Saddle(0,0),Maximum(9/4 , 2187/256)