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

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

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extreme f(x)=x^2+1/(x^2)

extreme points

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

Minimum (- 1, 2), Minimum (1, 2)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

x^{2} + \frac{1}{x ^{2}} : 2

Minimum (- 1, 2)

Plug

x = 1

into

x^{2} + \frac{1}{x ^{2}} : 2

Minimum (1, 2)

Minimum (- 1, 2), Minimum (1, 2)

f (x) = 5 x^{\frac{2}{3}} - x^{\frac{5}{3}}

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

f (x, y) = 4 x^{2} + y^{2}

f (x, y) = 3 x^{2} y - y^{3} + 36 x - 15 y + 18

f (x, y) = x y (1 - x - y)

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