What is the extreme 6x^2-2x^4 ?

The extreme 6x^2-2x^4 is Maximum(-sqrt(3/2), 9/2),Minimum(0,0),Maximum(sqrt(3/2), 9/2)

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extreme 6x^2-2x^4

extreme

Maximum (- \frac{3}{2}, \frac{9}{2}), Minimum (0, 0), Maximum (\frac{3}{2}, \frac{9}{2})

Solution steps

f^{'} (x) = 12 x - 8 x^{3}

Find intervals:

Increasing

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

Decreasing

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

Increasing

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

Decreasing

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

Plug

x = - \frac{3}{2}

into

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

Maximum (- \frac{3}{2}, \frac{9}{2})

Plug

x = 0

into

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

Minimum (0, 0)

Plug

x = \frac{3}{2}

into

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

Maximum (\frac{3}{2}, \frac{9}{2})

Maximum (- \frac{3}{2}, \frac{9}{2}), Minimum (0, 0), Maximum (\frac{3}{2}, \frac{9}{2})

What is the extreme 6x^2-2x^4 ?
The extreme 6x^2-2x^4 is Maximum(-sqrt(3/2), 9/2),Minimum(0,0),Maximum(sqrt(3/2), 9/2)