AP EAMCET · Maths · Application of Derivatives
A particle moves along the curve \(y=x^2+2 x\). Then, the point on the curve such that \(x\) and \(y\) coordinates of the particle change with the same rate is
- A \((1,3)\)
- B \(\left(\frac{1}{2}, \frac{5}{2}\right)\)
- C \(\left(-\frac{1}{2},-\frac{3}{4}\right)\)
- D \((-1,-1)\)
Answer & Solution
Correct Answer
(C) \(\left(-\frac{1}{2},-\frac{3}{4}\right)\)
Step-by-step Solution
Detailed explanation
Given equation of curve is \[ y=x^2+2 x \] On differentiating both sides w.r.t. \(t\), we get \[ \frac{d y}{d t}=(2 x+2) \frac{d x}{d t} \] \[ \begin{aligned} \Rightarrow & & 2 x & =-1 \\ \Rightarrow & & x & =-1 / 2, y=-3 / 4 \end{aligned} \] \(\therefore\) Point on the curve is…
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