What is the extreme f(x)=(x^6}{10}-\frac{2x^5)/3 ?

The extreme f(x)=(x^6}{10}-\frac{2x^5)/3 is Saddle(0,0),Minimum(50/9 ,-312500000/531441)

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extreme f(x)=(x^6}{10}-\frac{2x^5)/3

extreme

Saddle (0, 0), Minimum (\frac{50}{9}, - \frac{312500000}{531441})

Solution steps

f^{'} (x) = \frac{3 x ^{5}}{5} - \frac{10 x ^{4}}{3}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{50}{9},

Increasing

: \frac{50}{9} < x < \infty

Plug

x = 0

into

\frac{x ^{6}}{10} - \frac{2 x ^{5}}{3} : 0

Saddle (0, 0)

Plug

x = \frac{50}{9}

into

\frac{x ^{6}}{10} - \frac{2 x ^{5}}{3} : - \frac{312500000}{531441}

Minimum (\frac{50}{9}, - \frac{312500000}{531441})

Saddle (0, 0), Minimum (\frac{50}{9}, - \frac{312500000}{531441})

What is the extreme f(x)=(x^6}{10}-\frac{2x^5)/3 ?
The extreme f(x)=(x^6}{10}-\frac{2x^5)/3 is Saddle(0,0),Minimum(50/9 ,-312500000/531441)