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Thread: If P=20t+45t^2 find dp/dt - can someone please check my working and answer? :)

  1. #1
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    If P=20t+45t^2 find dp/dt - can someone please check my working and answer? :)

    If P=20t+45t^2 find dp/dt - can someone please check my working and answer? :)-math1.jpg

    New to the subject. Help would be much appreciated
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    Re: If P=20t+45t^2 find dp/dt - can someone please check my working and answer? :)

    $p=20t + 45 t^2$

    $\dfrac{d}{dt} c t^n = c n t^{n-1}$

    $\dfrac{dp}{dt}=20 + 90 t$
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    Re: If P=20t+45t^2 find dp/dt - can someone please check my working and answer? :)

    I presume that you are required here to use the "difference quotient" definition. That is that the derivative is defined as \lim_{dx\to 0} \frac{P(t+ dt)- P(t)}{dx} (Many people do not like using "dt" here, reserving that for after the limit). Yes, with P(t)= 20t+ 45t^2, P(t+ dt)= 20(t+ dt)+ 45(t+ dt)^2.

    But then you have an error in your very next line. You have 20(t+ dt) equal to 20t+ dt. It should be 20t+ 20dt. So P(t+ dt)= 20t+ 20dt+ 45t^2+ 90t dt+ dt^2

    And subtracting P(t)= 20t+ 45t^2 from that leaves P(t+ dt)- P(t)= 20dt+ 90 t dt+ dt^2. You have only "dt" rather than "20dt". Finally, dividing by "dt", \frac{P(t+dt)- P(t)}{dt}= 20+ 90t+ dt and the limit of that as dt goes to 0 is 20+ 90t.
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    Re: If P=20t+45t^2 find dp/dt - can someone please check my working and answer? :)

    As your Q. stands, there is not a specific & stated requirement to use the "difference quotient" definition. Hence, the solution provided in post #2 is adequate. Although the solution given in post #3 is mathematically valid, it is based on an unjustified presumption and is akin to using a sledge hammer to crack a nut.

    Al.
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    Re: If P=20t+45t^2 find dp/dt - can someone please check my working and answer? :)

    Quote Originally Posted by Skywave View Post
    As your Q. stands, there is not a specific & stated requirement to use the "difference quotient" definition. Hence, the solution provided in post #2 is adequate. Although the solution given in post #3 is mathematically valid, it is based on an unjustified presumption and is akin to using a sledge hammer to crack a nut.

    Al.
    The student's attempt to do the problem is, in fact, your sledge hammer. And as this is likely the start of a summer course it's probably the only method (s)he knows.

    -Dan
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    Re: If P=20t+45t^2 find dp/dt - can someone please check my working and answer? :)

    Quote Originally Posted by topsquark View Post
    The student's attempt to do the problem is, in fact, your sledge hammer.
    And as this is likely the start of a summer course it's probably the only method (s)he knows.
    -Dan
    Your first sentence carries no logic at all!
    And your second sentence needs to be proven, before it can claimed to be valid!

    Al. / Skywave
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    Re: If P=20t+45t^2 find dp/dt - can someone please check my working and answer? :)

    Thanks for the help everyone guess I made a mistake. I've since learned the power rule for differentiation which is much easier. I should have looked into that earlier.
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