Minima and maxima occur when the derivative is zero, also vertical tangeants when the derivative doesn't exist. (I think I remembered that last part right)

so dy/dt = ; solving for zero gives t=-2/3. I think t=0 is also an extrema point but I'll leave that to you to check out. Also check your answer using a graphing calculator or software such as MATLAB. If you need further help, please ask and I'll detail the answer further.