Assume that exists and let c be a point of inflection of . (a) Use the method of Exercise 62 to prove that the

Assume that ƒ" exists and let c be a point of inflection of ƒ.

(a) Use the method of Exercise 62 to prove that the tangent line at x = c crosses the graph (Figure 21). Show that G(x) changes sign at x = c.

Data From Exercise 62

Prove that if ƒ" exists and ƒ"(x) > 0 for all x, then the graph of ƒ“sits above” its tangent lines.

(b) Verify this conclusion for ƒ(x) = x / 3x² + 1 by graphing ƒ and the tangent line at each inflection point on the same set of axes.