Find the points on the graph of y2 = x3 3x + 1 (Figure 10) where the tangent line is
Chapter 3, Problem 61(choose chapter or problem)
Find the points on the graph of y2 = x3 3x + 1 (Figure 10) where the tangent line is horizontal. (a) First show that 2yy = 3x2 3, where y = dy/dx. (b) Do not solve for y . Rather, set y = 0 and solve for x. This yields two values of x where the slope may be zero. (c) Show that the positive value of x does not correspond to a point on the graph. (d) The negative value corresponds to the two points on the graph where the tangent line is horizontal. Find their coordinates. 2
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