# A problem featuring area of a square and rate of change.

Printable View

• Oct 10th 2010, 06:22 PM
Chimera
A problem featuring area of a square and rate of change.
the length of a rectangle is given by 6t+ 5 and its height is $\displaystyle sqrt(t)$, where t is time in seconds and the dimensions are in centimeters. Find the rate of change with respect to time.

I am not really quite sure how to do rate of change.. I have read over the examples given for rate of change in the book however, it seems vague and borderline unrelated.. Their problem was dealing with speed and velocity..
• Oct 10th 2010, 07:05 PM
Prove It
Are you finding the rate of change of the area?

$\displaystyle A = (6t+5)\sqrt{t}$.

The rate of change of the area is the derivative of this function.
• Oct 10th 2010, 07:11 PM
Chimera
I gave you everything the book gave me to be honest.

So from here I am guessing I would just use the product rule to find the derivative from what you gave me?
• Oct 10th 2010, 07:20 PM
Scopur
The derivative IS the rate of change $\displaystyle dy/dx$ is the rate of change of y with respect to the change in x... in this case your independent variable is time. so just find $\displaystyle dA/dt$

Yes use the product rule.