hi, i'm starting to look at work on rates of change and was wondering if someone could explain something to me.
the example question goes like this:
the volume, $\displaystyle Vm^3$ of water is given by $\displaystyle V = t^3 - 5t^2 + 6t + 2$. find the rate of change of volume with respect to time after 0.5 hours
it then goes on to $\displaystyle \frac{dV}{dt} = 3t^2 - 10t + 6$ and explains that:
when t = 0.5 $\displaystyle \frac{dV}{dt} = 3(0.5)^2 - 10(0.5) + 6 = 1.75 \implies$ after 0.5 hours the volume is increasing at a rate of $\displaystyle 1.75m^3h^-1$
i don't understand where the power of minus 1 $\displaystyle (h^-1)$ comes from?
can someone please explain this? thankyou