The velocity v of a particle is given by the equation `v=6t^2-6t^3`, where v is in `ms^-1`, `t` is the instant of time in seconds while 6 and 6 are suitable dimensional constants. At what values of t will the velocity be maximum and minimum? Determine these maximum and minimum values of the velocity.

Explanation

To find the values of \( t \) at which the velocity \( v \) is maximum and minimum, we will follow these steps:

### Step 1: Differentiate the velocity function
Given the velocity function:
\[ v = 6t^2 - 6t^3 \]
we need to differentiate \( v \) with respect to \( t \):
...