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 maximum and minimum values of the velocity given by the equation \( v = 6t^2 - 6t^3 \), we will follow these steps:

### Step 1: Differentiate the velocity function
We start by differentiating the velocity function with respect to time \( t \).

\[ \frac{dv}{dt} = \frac{d}{dt}(6t^2 - 6t^3) \]
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