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letamp;#39;s consider the function f of x equals e to the X and plot it on the axis here we can draw the tangent line to the curve which looks like the curve locally and whose slope is the instant rate of change of the Curve we can compute the slope of this line and we see that here itamp;#39;s .08 as we move the point along the curve we see that the slopes of the tangent lines get larger in fact something even more interesting happens in this example if we also plot the y coordinate of the point we see that as the point moves along the curve the slope of the tangent line actually equals the Y value we can take this one step further where we plot a new graph on a new set of axes here the Y value will be the slope of the tangent line from the first graph as we move the point along the curve we map out this graph the function f of x equals e to the x is a special function because its derivative or its slope function f Prime of X is also e to the x
