AP EAMCET · Maths · Application of Derivatives
If the normal drawn at a point \(P\) on the curve \(3 y=6 x-5 x^3\) passes through \((0,0)\), then the positive integral value of the abscissa of the point \(P\) is
- A \(1\)
- B \(\frac{2}{3}\)
- C \(\frac{1}{3}\)
- D \(-\frac{2}{3}\)
Answer & Solution
Correct Answer
(A) \(1\)
Step-by-step Solution
Detailed explanation
Given curve \(3 y=6 x-5 x^3\) \(\Rightarrow \quad \frac{d y}{d x}=2-5 x^2\) Slope of normal \(=\frac{-1}{2-5 x^2}\) Equation of normal with slope \(\frac{-1}{2-5 x^2}\) passing through origin \((0,0)\). \(\frac{\left(y-y_1\right)}{x-x_1}=m\)…
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