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Popular >

monotone f(x)=(x^3)/(x^2-4)

Solution

monotone intervals

f (x) = \frac{x ^{3}}{x ^{2} - 4}

Solution

Increasing : - \infty < x < - 23, Decreasing : - 23 < x < - 2, Decreasing : - 2 < x < 0, Decreasing : 0 < x < 2, Decreasing : 2 < x < 23, Increasing : 23 < x < \infty

Solution steps

f^{'} (x) = \frac{x ^{4} - 12 x ^{2}}{( x ^{2} - 4 ) ^{2}}

Find intervals:

Increasing

: - \infty < x < - 23,

Decreasing

: - 23 < x < - 2,

Decreasing

: - 2 < x < 0,

Decreasing

: 0 < x < 2,

Decreasing

: 2 < x < 23,

Increasing

: 23 < x < \infty

Increasing : - \infty < x < - 23, Decreasing : - 23 < x < - 2, Decreasing : - 2 < x < 0, Decreasing : 0 < x < 2, Decreasing : 2 < x < 23, Increasing : 23 < x < \infty

Graph

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Frequently Asked Questions (FAQ)

What is the monotone f(x)=(x^3)/(x^2-4) ?
The monotone f(x)=(x^3)/(x^2-4) is