Question

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

• A. $-1$
• B. $\pi$
• C. $-\pi$
• D. $0$
• E. $1$

Answer 1

Answer: (A)

$-1$

Answer 2

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}$

                   $⇒ ∝=-1$