Assume that exists and let c be a point of inflection of . (a) Use the
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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.
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a Let Gx fx fcx c fc Then as in Exercise 62 Gc Gc 0 and Gx fx If fx changes from positive to nega...View the full answer
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