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

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

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

extreme points

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

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

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

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

Minimum (- 1, 2)

Plug

x = 1

into

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

Minimum (1, 2)

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

e^{3 x^{2}}

f (x) = 4 - 5 x^{2}

f (x) = 12 + x + 24 - x

f (x) = - \frac{1}{12} x^{3} + x - \frac{1}{3}

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

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