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12 Nov 2019
My Not EXAMPLE 1 Find an equation of the tangent line to the function y 4x4 at the point P(1, 4). SOLUTION We will be able to find an equation of the tangent line t as soon as we know its slope m. The difficulty observe that we can compute an approximation to m by choosing a nearby point Qix, ax) on the graph (as in the figure) and computing the slope mpo of the secant line PO. [A secant line, from the Latin word secans, meaning cutting, is a line that cuts (intersects) a curve more than once.] is that we know only one point, P, on t, whereas we need two points to compute the slope. But we choose x# 1 so that Q* P. Then, 4x44 x-1 PQ For instance, for the point Q(1.5, 20.25) we have .5 The tables below show the values of mpo for several values of x close to 1. The closer Q is to P, the closer x is to 1 and, it appears from the tables, the closer mpo is to tangent line t should be m = This suggests that the slope of the 2 60 04 1.5 32.5 57.5 1.1 18.5649 13.756 1.01 |16.242 99 15.762 1.001 16.024 999 15.976 we say that the slope of the tangent line is the limit of the slopes of the secant lines, and we express this
My Not EXAMPLE 1 Find an equation of the tangent line to the function y 4x4 at the point P(1, 4). SOLUTION We will be able to find an equation of the tangent line t as soon as we know its slope m. The difficulty observe that we can compute an approximation to m by choosing a nearby point Qix, ax) on the graph (as in the figure) and computing the slope mpo of the secant line PO. [A secant line, from the Latin word secans, meaning cutting, is a line that cuts (intersects) a curve more than once.] is that we know only one point, P, on t, whereas we need two points to compute the slope. But we choose x# 1 so that Q* P. Then, 4x44 x-1 PQ For instance, for the point Q(1.5, 20.25) we have .5 The tables below show the values of mpo for several values of x close to 1. The closer Q is to P, the closer x is to 1 and, it appears from the tables, the closer mpo is to tangent line t should be m = This suggests that the slope of the 2 60 04 1.5 32.5 57.5 1.1 18.5649 13.756 1.01 |16.242 99 15.762 1.001 16.024 999 15.976 we say that the slope of the tangent line is the limit of the slopes of the secant lines, and we express this
Beverley SmithLv2
3 Nov 2019