If $x=2at, y =at^2, $ where 'a' is a constant, then $\frac{d^2y}{dx^2}$ at x= 2 is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $\frac{1}{2a}$
$x=2at$
$\frac{dx}{dt}=2a$
$y=at^2$
$\frac{dy}{dt}=2at$
$\frac{dy}{dx}=t⇒\frac{d^2y}{dx^2}=\frac{dt}{dx}=\frac{1}{2a}$
at $x=2$
$\frac{d^2y}{dx^2}=\frac{1}{2a}$