AP EAMCET · Maths · Differentiation
If \(x=a t^2\) and \(y=2 a t\), then \(\frac{d^2 y}{d x^2}\) at \(t=\frac{1}{2}\) is
- A \(-\frac{2}{a}\)
- B \(\frac{4}{a}\)
- C \(\frac{8}{a}\)
- D \(-\frac{4}{a}\)
Answer & Solution
Correct Answer
(D) \(-\frac{4}{a}\)
Step-by-step Solution
Detailed explanation
We have, \(x=a t^2\) \(\Rightarrow \quad \frac{d x}{d t}=2 a t \quad \Rightarrow \quad \frac{d t}{d x}=\frac{1}{2 a t}\) and \(y=2 a t \Rightarrow \frac{d y}{d t}=2 a\) \(\therefore \quad \frac{d y}{d x}=\frac{d y / d t}{d x / d t}=\frac{2 a}{2 a t}=\frac{1}{t}\) Differentiating…
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