Sketch the lines tangent to the curve shown in Fig. 7 at x =1, 2 and 3.

Question

Estimate the slope of each of the tangent lines you drew.

Answer 1

At x=1, the curve is almost linear so if you draw a line along the curve passing through the point on the curve where x=1, that line will be the tangent with a slope of about 2/2=1 (using the dotted squares as a guide to measurement).

A horizontal line at x=2 has a slope of zero.

At x=2, as at x=1, a line can be drawn along the curve. Its slope would be about -1 (the line leans backwards).

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