Find the points on the graph of y² = x³ − 3x + 1 (Figure 5) 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.

Transcribed Image Text:

-2 -1 y 2- -2- 1 +X 2