What is the extreme y=x^4-9x^2 ?

The extreme y=x^4-9x^2 is Minimum(-3/(sqrt(2)),-81/4),Maximum(0,0),Minimum(3/(sqrt(2)),-81/4)

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extreme y=x^4-9x^2

extreme

Minimum (- \frac{3}{2}, - \frac{81}{4}), Maximum (0, 0), Minimum (\frac{3}{2}, - \frac{81}{4})

Solution steps

f^{'} (x) = 4 x^{3} - 18 x

Find intervals:

Decreasing

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

Increasing

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

Decreasing

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

Increasing

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

Plug

x = - \frac{3}{2}

into

x^{4} - 9 x^{2} : - \frac{81}{4}

Minimum (- \frac{3}{2}, - \frac{81}{4})

Plug

x = 0

into

x^{4} - 9 x^{2} : 0

Maximum (0, 0)

Plug

x = \frac{3}{2}

into

x^{4} - 9 x^{2} : - \frac{81}{4}

Minimum (\frac{3}{2}, - \frac{81}{4})

Minimum (- \frac{3}{2}, - \frac{81}{4}), Maximum (0, 0), Minimum (\frac{3}{2}, - \frac{81}{4})

What is the extreme y=x^4-9x^2 ?
The extreme y=x^4-9x^2 is Minimum(-3/(sqrt(2)),-81/4),Maximum(0,0),Minimum(3/(sqrt(2)),-81/4)