Determine max/min speeds of trochoid Find the minimum and maximum speeds of the point of a trochoid and the locations where each occurs. I know a trochoid has equations $ (x)t = at - b \sin{t} $ ; $ y(t) = a- b \cos{t} $ for trochoid of radius a and b distance from center of circle (According to Wolfram) The only speed equation I'm familiar with thus far in my study of parametric equations is the arc-length equation. Would I set that equal to zero and then try and solve for a & b (cause I did and that gets really messy- not sure I know how to do that)? Any/all suggestions appreciated

For a parametric curve, the speed is just the modulus of the tangent vector, hence if $$\gamma(t)=(at-b\sin t,a-b\cos t)$$ we have $$ \dot{\gamma}(t) = (a-b\cos t,b\sin t) $$ so $$ v^2(t) = a^2+b^2-2ab\cos t $$ and the stationary points for $v(t)$ are the ones for which $\cos t=\pm 1$: $$ \max_{t} v(t) = |a+b|,$$ $$ \min_{t} v(t) = |a-b|.$$