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# Long description

This figure consists of a pair of Cartesian axes, labelled x and y. The diagram is focused on the upper-right quadrant. A curve representing part of the graph of an arbitrary real function f of x is drawn. (Actually, to facilitate the comprehensibility of the diagram, the graph is drawn to look like part of a cubic curve. It starts with positive gradient, then as x increases it reaches a local maximum, slopes down to a local minimum, and then slopes up again.) Three points are marked on the positive x-axis, labelled, from left to right, a, c and x. From each of these points a broken vertical line extends upwards to meet the curve. The three points where these three broken vertical lines meet the curve are marked with filled dots. The dot on the curve that lies above the point c on the x-axis is labelled with its coordinates, open bracket, c comma f of c, close bracket. This point is close to the local maximum of the graph. Through the point a line is drawn, tangent to the curve. A line segment is also drawn joining the other two points marked with dots on the curve (the points on the curve above the points a and x on the x-axis). This line segment is parallel to the tangent at c.