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The length of the longest interval, in w...

The length of the longest interval, in which the function `3sin x-4 sin^3x` is increasing is

Text Solution

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`f(x) = 3sinx - 4 sin^3 x = sin3x`
`f(x) = sin 3x`
`f'(x) = 3cos3x`
`f'(x) = 0`
`3cos 3x = 0`
`3x in (-pi/2 , pi/2)`
`x in (-pi/6, pi/6)`
longest interval `(pi/6 + pi/6) = pi/3`
...
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