What is the extreme f(x)= 1/2 x^4-4x^2+6 ?

The extreme f(x)= 1/2 x^4-4x^2+6 is Minimum(-2,-2),Maximum(0,6),Minimum(2,-2)

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extreme f(x)= 1/2 x^4-4x^2+6

extreme

Minimum (- 2, - 2), Maximum (0, 6), Minimum (2, - 2)

Solution steps

f^{'} (x) = 2 x^{3} - 8 x

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 2

into

\frac{1}{2} x^{4} - 4 x^{2} + 6 : - 2

Minimum (- 2, - 2)

Plug

x = 0

into

\frac{1}{2} x^{4} - 4 x^{2} + 6 : 6

Maximum (0, 6)

Plug

x = 2

into

\frac{1}{2} x^{4} - 4 x^{2} + 6 : - 2

Minimum (2, - 2)

Minimum (- 2, - 2), Maximum (0, 6), Minimum (2, - 2)

What is the extreme f(x)= 1/2 x^4-4x^2+6 ?
The extreme f(x)= 1/2 x^4-4x^2+6 is Minimum(-2,-2),Maximum(0,6),Minimum(2,-2)