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

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

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

extreme points

f (x) = x^{4} - 3 x^{3}

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

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

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

Increasing

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

Plug

x = 0

into

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

Saddle (0, 0)

Plug

x = \frac{9}{4}

into

x^{4} - 3 x^{3} : - \frac{2187}{256}

Minimum (\frac{9}{4}, - \frac{2187}{256})

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

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