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

The extreme f(x)=x^2+4/(x^2) is Minimum(-sqrt(2),4),Minimum(sqrt(2),4)

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extreme f(x)=x^2+4/(x^2)

extreme points

f (x) = x^{2} + \frac{4}{x ^{2}}

Minimum (- 2, 4), Minimum (2, 4)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 2

into

x^{2} + \frac{4}{x ^{2}} : 4

Minimum (- 2, 4)

Plug

x = 2

into

x^{2} + \frac{4}{x ^{2}} : 4

Minimum (2, 4)

Minimum (- 2, 4), Minimum (2, 4)

f (x) = - 5^{x}

y = 4 x - 4

(4, 1), (- 2, - 3)

f (x) = - x^{3} + 9 x^{2} - 2

f (x) = x^{2} - 10 x + 16

What is the extreme f(x)=x^2+4/(x^2) ?
The extreme f(x)=x^2+4/(x^2) is Minimum(-sqrt(2),4),Minimum(sqrt(2),4)