Question

A point moves along the curve y = √ x in such a way that the y-component of the position of the point is increasing at a rate of 2 units per second. At what rate is the x-component changing for each of the following values?

Answer 1

Answer:

The value of x component changes at a rate of $\frac{dx}{dt}=4\sqrt{x}$ units per second

Step-by-step explanation:

We are given that $y=x^{\frac{1}{2}}$

Differentiating on both sides with respect to time we get

$\frac{dy}{dt}=\frac{d\sqrt{x}}{dt}\\\\\frac{dy}{dt}=\frac{1}{2}x^{\frac{-1}{2}}(\frac{dx}{dt})\\\\\frac{dy}{dt}=\frac{1}{2\sqrt{x}}\frac{dx}{dt}$

It is given that $\frac{dy}{dt}=2units/sec$

Solving for $\frac{dx}{dt}$ we get

$\frac{dx}{dt}=\frac{dy}{dt}\times 2\sqrt{x}\\\\\frac{dx}{dt}=4\sqrt{x}$