# When calculus fails Related rates question

1. Feb 15, 2010

### koab1mjr

Hi I was just curious as to why calculus does not seem to work in the situation of area calculation. I came accross this doing some HW and noticed that the booked worked out a seemingly similar question in two seperate ways

First was predicitng the chance in the length of the hypotenuse. Using the pythagorean theorm take the derivative and your done. Plug in values and one has a relation that will predict the value of the hypotenuse given the orginal sides and their respective changes.

Now I had a similar problem with an area questions where I was trying to determine the new area given a defined change in the sides. Repeating as I have seen earliar. Take the derivative plug in values and ..... wrong answer.

So now I am curious to know the explanation why... Take area of a square given by a=s^2
the derivative is da = 2sds (I was taking the derivative in respects to time and eliminated dt) So given a 2x2 square with area 4, I want to predict the area if I increase the side by 1. Given the previous result it tells me that the da would be 4. But the next perfect square is 9.
I tried for triangles and as expected not correct. I just wanted to know why for some related rates calculus works and sometimes it doesn't.