I was doing some variable acceleration questions and I came across this one. I can't find a mark scheme anywhere or anything explaining how to find max acceleration in particular haha.
“A particle P starting from rest moves so that it's velocity v(ms-¹) at time t(s) is v = 12t² - 4t³
(ii) Find the maximum acceleration in the first 2 seconds of motion”
I've differentiated for dv/dt to get the formula for a (a=24t-12t²), but I've no clue how to find where the acceleration is at its highest ?? I've found the acceleration for t=0 and t=2, but surely there's another time you need to find it at? Losing my mind a bit haha, any help would be appreciated.