What is the extreme 1/5 x^5-3x^3 ?

The extreme 1/5 x^5-3x^3 is Maximum(-3, 162/5),Saddle(0,0),Minimum(3,-162/5)

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extreme 1/5 x^5-3x^3

extreme

Maximum (- 3, \frac{162}{5}), Saddle (0, 0), Minimum (3, - \frac{162}{5})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 3

into

\frac{1}{5} x^{5} - 3 x^{3} : \frac{162}{5}

Maximum (- 3, \frac{162}{5})

Plug

x = 0

into

\frac{1}{5} x^{5} - 3 x^{3} : 0

Saddle (0, 0)

Plug

x = 3

into

\frac{1}{5} x^{5} - 3 x^{3} : - \frac{162}{5}

Minimum (3, - \frac{162}{5})

Maximum (- 3, \frac{162}{5}), Saddle (0, 0), Minimum (3, - \frac{162}{5})

What is the extreme 1/5 x^5-3x^3 ?
The extreme 1/5 x^5-3x^3 is Maximum(-3, 162/5),Saddle(0,0),Minimum(3,-162/5)