The Length Of A Longest Interval In Which The Function 3 Sin x – 4Sin3x is Increasing Is

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Question

The length of a longest interval in which the function 3 sin x – 4Sin³x is increasing is

π/3
π/2
3π/2
π

easy

Solution

Correct option is

π/3

Since 3 sin x – 4 sin³x = sin 3x and sin 3x increases when 3x takes values from –π/2 to π/2 or x takes value from –π/6 to π/6. Thus, the length of the longest interval in which 3 sinx – 4 sin³x increases is π/6 – (–π/6) = π/3.