A particle is moving along the curve $y= 2 \sqrt{2 x + 2}$. As the particle passes through the point $(1, 4)$, its x-coordinate increases at a rate of $2$ units per second. Find the rate of change of the distance from the particle to the origin at this instant.
[Math] A particle is moving along the curve $y= 2 \sqrt{2 x + 2}$
calculus
Best Answer
Hint: The distance from the origin is given in general by $$D=\sqrt{x^2+y^2}=\sqrt{x^2+4(2x+2)}=\sqrt{x^2+8x+4}.$$ You're trying to find $\frac{dD}{dt}$ when $x=1,$ given that $\frac{dx}{dt}=2$ units per second when $x=1$. Any ideas how you might do that?