Question

# A particle moves along the curve $$6y = {x^3} + 2$$. Find the points on the curve at which y - coordinate is changing 2 times as fast as x - coordinate.

Solution

## we need to find coordinates of point where $$\dfrac{dy}{dt}=2\dfrac{dx}{dt}$$$$6y=x^3+2$$Differentiating on both sides$$6\dfrac{dy}{dt}=3x^2\dfrac{dx}{dt}$$$$6\times 2\dfrac{dx}{dt}=3x^2\dfrac{dx}{dt}$$$$x^2=4$$$$x=\pm 2$$If $$x=2\Rightarrow y=\dfrac{5}{3}$$if $$x=-2\Rightarrow y=-1$$Mathematics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More