Question:

Let \(f(x)=αsin^{2}3x.\) If \(f'(π/12)=-3\) ,then the value of \(α \) is_____.

Updated On: Aug 1, 2023

  • \(-1\)

  • \(\pi\)

  • \(-\pi\)

  • \(0\)

  • \(1\)

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The Correct Option is A

Solution and Explanation

Given that

\(f(x)=∝sin^{2}3x\)  and   \( f'(\dfrac{\pi}{12})=-3\)

Then ,

\(f'(x)=2×3∝sin3x.cos3x\)

\(f'(x)=6∝sin3x.cos3x\)

Now,  comparing the like terms we can write, 

\(x=\dfrac{\pi}{12}\)

So, 

     \(    f'(\dfrac{\pi}{12})=6∝sin3(\dfrac{\pi}{12}).cos3(\dfrac{\pi}{12})\)

                       \( ⇒       -3=6×∝×\dfrac{1}{√2}×\dfrac{1}{√2}\)

                       \(  ⇒           -3=6×∝×\dfrac{1}{2}\)

                       \(⇒ ∝=-1\)

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