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Measuring the Slope at a Point on a Curved Graph

Usually we will plot results which we expect to give us a straight line. If we plot a graph which we expect to give us a smooth curve, we might want to find the slope of the curve at a given point; for example, the slope of a displacement against time graph tells us the (instantaneous) velocity of the object.

To find the slope at a given point, draw a tangent to the curve at that point and then find the slope of the tangent in the usual way. This method is illustrated on the graph on the next page. A tangent to the curve has been drawn at x = 3s. The slope of the graph at this point is given by DELTA01y/DELTA01x = (approximately) 6ms-1.



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