What is the monotone x^4+x^3-3x^2+1 ?

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monotone x^4+x^3-3x^2+1

monotone intervals

x^{4} + x^{3} - 3 x^{2} + 1

Decreasing : - \infty < x < \frac{- 3 - 105}{8}, Increasing : \frac{- 3 - 105}{8} < x < 0, Decreasing : 0 < x < \frac{105 - 3}{8}, Increasing : \frac{105 - 3}{8} < x < \infty

Solution steps

f^{'} (x) = 4 x^{3} + 3 x^{2} - 6 x

Find intervals:

Decreasing

: - \infty < x < \frac{- 3 - 105}{8},

Increasing

: \frac{- 3 - 105}{8} < x < 0,

Decreasing

: 0 < x < \frac{105 - 3}{8},

Increasing

: \frac{105 - 3}{8} < x < \infty

Decreasing : - \infty < x < \frac{- 3 - 105}{8}, Increasing : \frac{- 3 - 105}{8} < x < 0, Decreasing : 0 < x < \frac{105 - 3}{8}, Increasing : \frac{105 - 3}{8} < x < \infty

f (x) = \frac{5}{2 x + 3}

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

\frac{2 x - 1}{x + 4}

f (x) = sin^{2} (5 x)

25 - x^{2} + x + 3