If $x=2at, y =at^2, $ where 'a' is a con

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Continuity and Differentiability

Question:

If $x=2at, y =at^2, $ where 'a' is a constant, then $\frac{d^2y}{dx^2}$ at x= 2 is :

Options:

$\frac{1}{4}$

$\frac{1}{2a}$

Correct Answer:

$\frac{1}{2a}$

Explanation:

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 $x=2$

$\frac{d^2y}{dx^2}=\frac{1}{2a}$