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24. If the second derivative f" exists at a value xo, show that f(xo + h) - 2f(xo) + f(xo − h) h² lim h→0 ƒ"(xo).

24. If the second derivative f" exists at a value xo, show that f(xo + h) - 2f(xo) + f(xo − h) h² lim h→0 ƒ"(xo).

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.CR: Chapter 3 Review
Problem 12CR: Determine whether each of the following statements is true or false and explain why. The derivative...
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24. If the second derivative f" exists at a value xo, show that f(xo + h) - 2f(xo) + f(xo - h) h² lim h→0 25. Suppose that f is defined by → Se-1/x² x → {0 f: x→ if x > 0, if x < 0. ƒ"(xo). (a) Show that f(n) (0) exists for every positive integer n (see Problem 7) and has the value 0.
Transcribed Image Text:24. If the second derivative f" exists at a value xo, show that f(xo + h) - 2f(xo) + f(xo - h) h² lim h→0 25. Suppose that f is defined by → Se-1/x² x → {0 f: x→ if x > 0, if x < 0. ƒ"(xo). (a) Show that f(n) (0) exists for every positive integer n (see Problem 7) and has the value 0.
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