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(adsbygoogle = window.adsbygoogle || []).push({});

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.

Thanks in advance

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# When calculus fails Related rates question

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