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To finding the the maxima and minima why do we equate the derivative of a function with zero and n0t with any other number like 10,100 ?

akanksha
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    Do you have any thoughts on this? What would it mean if the derivative of a function at a point was $10100$? What would the function look like at that point? Why couldn't that be a maximum? – crf Apr 15 '14 at 09:14
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    It looks like you haven't really understood what is behind the idea of derivative: give this a try http://en.wikipedia.org/wiki/Difference_quotient . Then think again at how the slope of a certain function looks like in the Neighbourhood of a local maximum/minimum and you should have your answer – b00n heT Apr 15 '14 at 09:16

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Think of derivatives as a slope of the function. In the maximum, the function is going horisontally and the derivative there is $0$.

Another way of looking is this: If the derivative is positive, then the function is increasing. If it is negative, the function is decreasing. In the maximum, the function is not rising and not falling, meaning the derivative is not negative and not positive. The only number like that is $0$.

5xum
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