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Popular >

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

Solution

extreme points

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

Solution

Maximum (0, 2)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 0,

Decreasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = 0

into

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

Maximum (0, 2)

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=(x^2)/(x^2-4)+2 ?
The extreme f(x)=(x^2)/(x^2-4)+2 is Maximum(0,2)