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Math Help - [SOLVED] rate question

  1. #1
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    [SOLVED] rate question

    Let r(t) be a differentiable function that is positive and increasing. The rate of increase of r^3 is equal to 12 times the rate of increase of r when r(t)=

    How would I go about setting this up to solve it? thanks for the help.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jst706 View Post
    Let r(t) be a differentiable function that is positive and increasing. The rate of increase of r^3 is equal to 12 times the rate of increase of r when r(t)=

    How would I go about setting this up to solve it? thanks for the help.
    when r(t) = what?

    you would set up something like 3r^2~r' = 12r', but more info is needed
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  3. #3
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    that is all the question says. It is a multiple choice question if that would help? The five choices are :

    the cube root of 4
    two
    the cube root of 12
    two times the square root of 3
    six

    The answer key says the answer is two, I guess taking the derivative of each and setting equal works since 3r^2=12 , thus r=2 thanks for the help
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jst706 View Post
    It answer key says the answer is two, but I dont know how to get there...would the proper way be to do 3r^2=12 , thus r=2
    yup, that's what i said. the equation 3r^2~r' = 12~r' must hold. so just solve for r
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