MHT CET · Maths · Application of Derivatives
A particle moves along a curve \(y=\frac{2 x^3-1}{3}\). The points on the curve at which the \(y\) co-ordinate is changing 18 times the \(x\) co-ordinate are
- A \(\left(-3,-\frac{55}{3}\right),\left(3,-\frac{53}{3}\right)\)
- B \(\left(-3, \frac{53}{3}\right),\left(3, \frac{55}{3}\right)\)
- C \(\left(-3,-\frac{53}{3}\right),\left(3, \frac{55}{3}\right)\)
- D \(\left(-3,-\frac{55}{3}\right),\left(3, \frac{53}{3}\right)\)
Answer & Solution
Correct Answer
(D) \(\left(-3,-\frac{55}{3}\right),\left(3, \frac{53}{3}\right)\)
Step-by-step Solution
Detailed explanation
\(\frac{dy}{dx} = \frac{d}{dx}\left(\frac{2 x^3-1}{3}\right) = \frac{1}{3}(6x^2) = 2x^2\) \(2x^2 = 18 \Rightarrow x^2 = 9 \Rightarrow x = \pm 3\)
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