# Math Help - [SOLVED] rate question

1. ## [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.

2. Originally Posted by jst706
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

3. 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

4. Originally Posted by jst706
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