Ok so I have a vector function:

r(t)=$\displaystyle <3cos(t) , 2sin(t)>$

Alright so I have to find the Max and Min for the magnitude of the acceleration.

The steps I was undergoing were:

1. I found the velocity vectorv(t)=$\displaystyle <-3sin(t) , 2cos(t)>$

2. I found the acceleration vectora(t)=$\displaystyle <-3cos(t) , -2sin(t)>$

and this is where I'm a little confused, so I have to find the function for the magnitude ofa(t) and then derive it, find the critical points and those will be my max and min. But the problem is that when I find the magnitude of acceleration it gives me a constant. (sin^2 + cos^2 = 1)

But that's the equation for an ellipse so the acceleration is not constant... so what am i doing wrong?

EDIT: Oh crap I just realized what a dumb mistake I was making, the magnitude is not a constant, the coefficients are different, sin squared and cos squared can't be factored.