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Popular Functions >

monotone f(x)=x(x-1)(2x-1)

Solution

monotone intervals

f (x) = x (x - 1) (2 x - 1)

Solution

Increasing : - \infty < x < - \frac{1}{2 3} + \frac{1}{2}, Decreasing : - \frac{1}{2 3} + \frac{1}{2} < x < \frac{1}{2 3} + \frac{1}{2}, Increasing : \frac{1}{2 3} + \frac{1}{2} < x < \infty

Solution steps

f^{'} (x) = 6 x^{2} - 6 x + 1

Find intervals:

Increasing

: - \infty < x < - \frac{1}{2 3} + \frac{1}{2},

Decreasing

: - \frac{1}{2 3} + \frac{1}{2} < x < \frac{1}{2 3} + \frac{1}{2},

Increasing

: \frac{1}{2 3} + \frac{1}{2} < x < \infty

Increasing : - \infty < x < - \frac{1}{2 3} + \frac{1}{2}, Decreasing : - \frac{1}{2 3} + \frac{1}{2} < x < \frac{1}{2 3} + \frac{1}{2}, Increasing : \frac{1}{2 3} + \frac{1}{2} < x < \infty

Graph

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Frequently Asked Questions (FAQ)

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