1. ## rate of change

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

2. per hour! (same as /h)

3. i understand that h stands for per hour. i meant the "to the power of minus 1" part. why is it to the power of minus one?

also how do you write it in latex so that the 1 appears small and at the top like in $\displaystyle t^3$. it comes out big with minus 1 $\displaystyle h^-1$
cheers

4. use the 'hat' symbol (shift 6?) like in excel etc. i.e. h^{-1} oh yes and use curly braces if the power contains more than one character

h means hour, power minus one means per

5. ah i see. thanks