What is the extreme f(x)=x^4-72x^2 ?

The extreme f(x)=x^4-72x^2 is Minimum(-6,-1296),Maximum(0,0),Minimum(6,-1296)

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extreme f(x)=x^4-72x^2

extreme points

f (x) = x^{4} - 72 x^{2}

Minimum (- 6, - 1296), Maximum (0, 0), Minimum (6, - 1296)

Solution steps

f^{'} (x) = 4 x^{3} - 144 x

Find intervals:

Decreasing

: - \infty < x < - 6,

Increasing

: - 6 < x < 0,

Decreasing

: 0 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = - 6

into

x^{4} - 72 x^{2} : - 1296

Minimum (- 6, - 1296)

Plug

x = 0

into

x^{4} - 72 x^{2} : 0

Maximum (0, 0)

Plug

x = 6

into

x^{4} - 72 x^{2} : - 1296

Minimum (6, - 1296)

Minimum (- 6, - 1296), Maximum (0, 0), Minimum (6, - 1296)

f (x) = - 3 x^{4} ln (3 x), (0, 4)

(2 x - 1)^{2}

f (x, y) = 5 x^{2} - x y + 3 y^{2}

f (t) = t + (t^{2} + t) \cdot u (t - 3) + (t - t^{2}) u (t - 5)

What is the extreme f(x)=x^4-72x^2 ?
The extreme f(x)=x^4-72x^2 is Minimum(-6,-1296),Maximum(0,0),Minimum(6,-1296)