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

The extreme f(x)=(x^4)/4-x^3 is Saddle(0,0),Minimum(3,-27/4)

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

extreme points

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

Saddle (0, 0), Minimum (3, - \frac{27}{4})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 0

into

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

Saddle (0, 0)

Plug

x = 3

into

\frac{x ^{4}}{4} - x^{3} : - \frac{27}{4}

Minimum (3, - \frac{27}{4})

Saddle (0, 0), Minimum (3, - \frac{27}{4})

What is the extreme f(x)=(x^4)/4-x^3 ?
The extreme f(x)=(x^4)/4-x^3 is Saddle(0,0),Minimum(3,-27/4)