Question

Let $f(x)=αsin^23x$ .If $f ′(\dfrac{π}{12})$ = $−3$,then the value of $α$ is

• A. $-1$
• B. $\pi$
• C. $\dfrac{\pi}{2}$
• D. $1$
• E. $-\pi$

Answer 1

Answer: (A)

$-1$

Answer 2

Given that:

$f(x) = α sin^23$

derivate both side with respect to $x$$$

$\therefore f' (x) = 3α sin 6x$

$f ′ (\dfrac{π}{12}) = −3$ $\therefore$ ($Sin(\dfrac{\pi}{2}=1)$)

$3α sin(\dfrac{π}{2}) = −3$

$α = −1$ (_Ans)