Hi everyone. I'm currently working on a velocity problem. Here's what I did:

A particle moves on the x-axis so that its velocity at any time t≥0 is given by v(t)=12t^2-36t+15. At t = 1, the particle is at the origin

Find the maximum velocity of the particle for 0≤t≤2.

V'=24t-36

24t-36=0

6(4t-6)=0

t=3/2

I drew a sign chart, and I found that 3/2 is actually the minimum. How can I get the maximum velocity?

Thanks a lot.