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What is the length of the longest interval in which the function f(x) = 3sin x – 4sin3 x is increasing?

What is the length of the longest interval in which the function f(x) = 3sin x – 4sin3 x is increasing? Correct Answer <span class="math-tex">\(\frac{{\rm{\pi }}}{3}\)</span>

Concept:

Trigonometric formulas used:

  • sin 3x = 3sin x – 4sin3 x


Calculation:

Given: f(x) = 3sin x – 4sin3 x

We know that, sin 3x = 3sin x – 4sin3 x

So, f(x) = 3 sin x – 4 sin3 x = sin 3x

We know that, sin 3x is a periodic function.

As we know Sin x is a periodic function   

Since here the function is Sin 3x the range becomes

So, sin 3x increases from –π/6 to π/6.

∴ The length of the increasing interval = π/6 – (-π/6) = π/3 

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