If x^2 +y^2 =25 and dy/dt = 6, find dx/dt when y = 4
When I did this, I got positive and negative three, but that can't be right. What is the right way to do this?
$\displaystyle x^2+y^2=5^2$
is a circle centred at the origin (0,0) with radius=5.
Hence, when y=4,
$\displaystyle x^2+16=25\ \Rightarrow\ x^2=9\ \Rightarrow\ x=\pm3$
The radius is unchanging..
$\displaystyle \frac{d}{dt}\left(x^2+y^2\right)=0$
$\displaystyle \frac{dx}{dt}\frac{d}{dx}x^2+\frac{dy}{dt}\frac{d} {dt}y^2=0$
$\displaystyle 2x\frac{dx}{dt}=-2y\frac{dy}{dt}$
Solve this at (3,4) and (-3,4).