What is the monotone (2x-1)^7(x+5)^6 ?

The monotone (2x-1)^7(x+5)^6 is

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monotone (2x-1)^7(x+5)^6

monotone intervals

(2 x - 1)^{7} (x + 5)^{6}

Increasing : - \infty < x < - 5, Decreasing : - 5 < x < - \frac{32}{13}, Increasing : - \frac{32}{13} < x < \frac{1}{2}, Increasing : \frac{1}{2} < x < \infty

Solution steps

f^{'} (x) = 2 (x + 5)^{5} (2 x - 1)^{6} (13 x + 32)

Find intervals:

Increasing

: - \infty < x < - 5,

Decreasing

: - 5 < x < - \frac{32}{13},

Increasing

: - \frac{32}{13} < x < \frac{1}{2},

Increasing

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

Increasing : - \infty < x < - 5, Decreasing : - 5 < x < - \frac{32}{13}, Increasing : - \frac{32}{13} < x < \frac{1}{2}, Increasing : \frac{1}{2} < x < \infty

\frac{2 x + 1}{3 x ^{2}}

f (x) = \frac{( x + 1 ) ^{2}}{2 x - 1}

y = - 5 sin (π - 4 x) + 1

\frac{x + 4}{x - 5}

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