# Math Help - Significance of dz/dt=0 for z=sqrt(x^2 + y^2)

1. ## Significance of dz/dt=0 for z=sqrt(x^2 + y^2)

For the curve in the (x,y) plane,
$z=\sqrt{x^2+y^2}$
when $\frac{dx}{dt} = -5sin (t)$ , $\frac{dy}{dt} = 12 cos (t)$ , $x(0) = 5$ , $y(0)=0$

I calculated $\frac{dz}{dt} = \frac{12 y cos (t) - 5 x sin (t)}{\sqrt{x^2+y^2}}=0$ at the point when $t=\frac{\pi}{2}$ , $x=0$, $y= 12$.

Can someone help me explain the significance of this answer (when $\frac{d^2 z}{dt^2} = \frac{-110}{12}$ at $t=\frac{\pi}{2}$) ????

2. ## Re: Significance of dz/dt=0 for z=sqrt(x^2 + y^2)

If a second derivative is negative at a critical point, then you have a local maximum.