What is the extreme f(x)=x^6-x^4 ?

The extreme f(x)=x^6-x^4 is Minimum(-sqrt(2/3),-4/27),Maximum(0,0),Minimum(sqrt(2/3),-4/27)

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extreme f(x)=x^6-x^4

extreme

Minimum (- \frac{2}{3}, - \frac{4}{27}), Maximum (0, 0), Minimum (\frac{2}{3}, - \frac{4}{27})

Solution steps

f^{'} (x) = 6 x^{5} - 4 x^{3}

Find intervals:

Decreasing

: - \infty < x < - \frac{2}{3},

Increasing

: - \frac{2}{3} < x < 0,

Decreasing

: 0 < x < \frac{2}{3},

Increasing

: \frac{2}{3} < x < \infty

Plug

x = - \frac{2}{3}

into

x^{6} - x^{4} : - \frac{4}{27}

Minimum (- \frac{2}{3}, - \frac{4}{27})

Plug

x = 0

into

x^{6} - x^{4} : 0

Maximum (0, 0)

Plug

x = \frac{2}{3}

into

x^{6} - x^{4} : - \frac{4}{27}

Minimum (\frac{2}{3}, - \frac{4}{27})

Minimum (- \frac{2}{3}, - \frac{4}{27}), Maximum (0, 0), Minimum (\frac{2}{3}, - \frac{4}{27})

What is the extreme f(x)=x^6-x^4 ?
The extreme f(x)=x^6-x^4 is Minimum(-sqrt(2/3),-4/27),Maximum(0,0),Minimum(sqrt(2/3),-4/27)