What is the extreme f(x)=9x^{10}-3x^9 ?

The extreme f(x)=9x^{10}-3x^9 is Saddle(0,0),Minimum(3/10 ,(531441)/(10^{10)}-59049/1000000000)

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extreme f(x)=9x^{10}-3x^9

extreme

Saddle (0, 0), Minimum (\frac{3}{10}, \frac{531441}{1 0 ^{10}} - \frac{59049}{1000000000})

Solution steps

Find the critical points:

x = 0, x = \frac{3}{10}

Domain of

9 x^{10} - 3 x^{9} : - \infty < x < \infty

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{3}{10},

Increasing

: \frac{3}{10} < x < \infty

Plug the extreme point

x = 0

into

9 x^{10} - 3 x^{9} \Rightarrow y = 0

Saddle (0, 0)

Plug the extreme point

x = \frac{3}{10}

into

9 x^{10} - 3 x^{9} \Rightarrow y = \frac{531441}{1 0 ^{10}} - \frac{59049}{1000000000}

Minimum (\frac{3}{10}, \frac{531441}{1 0 ^{10}} - \frac{59049}{1000000000})

Saddle (0, 0), Minimum (\frac{3}{10}, \frac{531441}{1 0 ^{10}} - \frac{59049}{1000000000})

What is the extreme f(x)=9x^{10}-3x^9 ?
The extreme f(x)=9x^{10}-3x^9 is Saddle(0,0),Minimum(3/10 ,(531441)/(10^{10)}-59049/1000000000)