What is the extreme f(x)=7x^4-6x^2-6 ?

The extreme f(x)=7x^4-6x^2-6 is Minimum(-sqrt(3/7),-51/7),Maximum(0,-6),Minimum(sqrt(3/7),-51/7)

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extreme f(x)=7x^4-6x^2-6

extreme

Minimum (- \frac{3}{7}, - \frac{51}{7}), Maximum (0, - 6), Minimum (\frac{3}{7}, - \frac{51}{7})

Solution steps

f^{'} (x) = 28 x^{3} - 12 x

Find intervals:

Decreasing

: - \infty < x < - \frac{3}{7},

Increasing

: - \frac{3}{7} < x < 0,

Decreasing

: 0 < x < \frac{3}{7},

Increasing

: \frac{3}{7} < x < \infty

Plug

x = - \frac{3}{7}

into

7 x^{4} - 6 x^{2} - 6 : - \frac{51}{7}

Minimum (- \frac{3}{7}, - \frac{51}{7})

Plug

x = 0

into

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

Maximum (0, - 6)

Plug

x = \frac{3}{7}

into

7 x^{4} - 6 x^{2} - 6 : - \frac{51}{7}

Minimum (\frac{3}{7}, - \frac{51}{7})

Minimum (- \frac{3}{7}, - \frac{51}{7}), Maximum (0, - 6), Minimum (\frac{3}{7}, - \frac{51}{7})

What is the extreme f(x)=7x^4-6x^2-6 ?
The extreme f(x)=7x^4-6x^2-6 is Minimum(-sqrt(3/7),-51/7),Maximum(0,-6),Minimum(sqrt(3/7),-51/7)