WBJEE · Maths · Application of Derivatives
A point is in motion along a hyperbola \(y=\frac{10}{x}\) so that its abscissa \(x\) increases uniformly at a rate of 1 unit per second. Then, the rate of change of its ordinate when the point passes through (5,2)
- A increases at the rate of \(\frac{1}{2}\) unit per second
- B decreases at the rate of \(\frac{1}{2}\) unit per second
- C decreases at the rate of \(\frac{2}{5}\) unit per second
- D increases at the rate of \(\frac{2}{5}\) unit per second
Answer & Solution
Correct Answer
(C) decreases at the rate of \(\frac{2}{5}\) unit per second
Step-by-step Solution
Detailed explanation
We have, \[ \begin{array}{r} \frac{d x}{d t}=\operatorname{l and} y=\frac{10}{x} \\ \text { Now, } y=\frac{10}{x} \end{array} \] On differentiating both the sides w.r.t. \(t\), we get…
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