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Math Help - rate of change

  1. #1
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    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, Vm^3 of water is given by 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 \frac{dV}{dt} = 3t^2 - 10t + 6 and explains that:

    when t = 0.5 \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 1.75m^3h^-1

    i don't understand where the power of minus 1 (h^-1) comes from?

    can someone please explain this? thankyou
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  2. #2
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    per hour! (same as /h)
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  3. #3
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    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 t^3. it comes out big with minus 1 h^-1
    cheers
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  4. #4
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    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
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  5. #5
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    ah i see. thanks
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