COMEDK · Maths · 27. Application of Derivatives
The point on the curve \(y^{2}=x\), the tangent at which makes an angle \(45^{\circ}\) with \(X\)-axis is
- A \((1 / 2,1 / 4)\)
- B \((1 / 4,1 / 2)\)
- C \((1 / 2,1 / 2)\)
- D \((1 / 2,-1 / 2)\)
Answer & Solution
Correct Answer
(B) \((1 / 4,1 / 2)\)
Step-by-step Solution
Detailed explanation
We have, \[ \begin{gathered} y^{2}=x \\ \Rightarrow 2 y \frac{d y}{d x}=1 \Rightarrow \frac{d y}{d x}=\frac{1}{2 y} \end{gathered} \] Let the required point be \(\left(x_{1}, y_{1}\right)\), So, slope of tangent…
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