What is the extreme f(x)=(x^4-4x^3)/2 ?

The extreme f(x)=(x^4-4x^3)/2 is Saddle(0,0),Minimum(3,-27/2)

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extreme f(x)=(x^4-4x^3)/2

extreme

Saddle (0, 0), Minimum (3, - \frac{27}{2})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 0

into

\frac{x ^{4} - 4 x ^{3}}{2} : 0

Saddle (0, 0)

Plug

x = 3

into

\frac{x ^{4} - 4 x ^{3}}{2} : - \frac{27}{2}

Minimum (3, - \frac{27}{2})

Saddle (0, 0), Minimum (3, - \frac{27}{2})

What is the extreme f(x)=(x^4-4x^3)/2 ?
The extreme f(x)=(x^4-4x^3)/2 is Saddle(0,0),Minimum(3,-27/2)