First slide

Monotonicity

Question

$The length of a longest interval in which the function 3 \sin x - 4 \sin^{3} x is incresing is$

Moderate

A

$π / 3$
B

$π / 2$
C

$3 π / 2$
D

$π$

Solution

$\begin{array}{l} Since 3 \sin x - 4 \sin^{3} x = \sin 3 x and \sin 3 x increases when 3 x \\ takes values from - π / 2 to π / 2 or x takes values from \end{array}$
$\begin{array}{l} - π / 6 to π / 6 . Thus, the length of the longest interval in \\ which 3 \sin x - 4 \sin^{3} x increases is π / 6 - (- π / 6) = π / 3 . \end{array}$

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