Derivative

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"Derivative" is actually a word meaning slope, but not exactly the same sense of slope as you learned in algebra. In algebra you would find the slope of a straight line, and unless it were undefined it would be a single number. But look at the function :

How do we talk about the slope of this function? We can't represent it with a single number, because this function rises very slowly at first, then much more steeply later on. We get around this problem by talking about the slope of the curve at a point. We pick a point on the curve and draw a straight line which ...