What is the extreme f(x)=3x^2+(48)/(x^2) ?

The extreme f(x)=3x^2+(48)/(x^2) is Minimum(-2,24),Minimum(2,24)

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extreme f(x)=3x^2+(48)/(x^2)

extreme points

f (x) = 3 x^{2} + \frac{48}{x ^{2}}

Minimum (- 2, 24), Minimum (2, 24)

Solution steps

f^{'} (x) = 6 x - \frac{96}{x ^{3}}

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 2

into

3 x^{2} + \frac{48}{x ^{2}} : 24

Minimum (- 2, 24)

Plug

x = 2

into

3 x^{2} + \frac{48}{x ^{2}} : 24

Minimum (2, 24)

Minimum (- 2, 24), Minimum (2, 24)

f (x) = x^{3} - 3 x^{2} - 2 x - 1

f (x) = 2 x y - 15 y^{2}

f (x) = 6 sin (x) + cot (x)

f (x) = 2 + (x + 1)^{2}

f (x, y) = 5 + 4 x + 6 y - x^{2} - 3 y^{2}

What is the extreme f(x)=3x^2+(48)/(x^2) ?
The extreme f(x)=3x^2+(48)/(x^2) is Minimum(-2,24),Minimum(2,24)