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The functions f and g are continuous and differentiable for all values of x. The continuous function h(x) is given by h(x) = f(g(x)) - x². The table at the right gives values of f(x), f'(x), g(x), and g'(x) at selected values of x. X f(x) f'(x) g(x) g'(x) 2 38 0 6 -3 a. Explain why there must be a value x for 2 < x < 8 such that h(x) = 0. b. Show that there must be an x = c, 4 < c < 6, such that h' (c) = 0. 4 12 9 8 -4 6 9 -5 2 6 8 18 12 4 3

The functions f and g are continuous and differentiable for all values of x. The continuous function h(x) is given by h(x) = f(g(x)) - x². The table at the right gives values of f(x), f'(x), g(x), and g'(x) at selected values of x. X f(x) f'(x) g(x) g'(x) 2 38 0 6 -3 a. Explain why there must be a value x for 2 < x < 8 such that h(x) = 0. b. Show that there must be an x = c, 4 < c < 6, such that h' (c) = 0. 4 12 9 8 -4 6 9 -5 2 6 8 18 12 4 3

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The functions f and g are continuous and differentiable for all values of x. The continuous function h(x) is given by h(x) = f(g(x)) — x². The table at the right gives values of f(x), ƒ'(x), g(x), and g'(x) at selected values of x. f(x) f'(x) g(x) 2 38 0 6 -3 a. Explain why there must be a value x for 2 < x < 8 such that h(x) = 0. b. Show that there must be an x = c, 4 < c < 6, such that h'(c) = 0. 4 12 9 8 6 9 -5 2 6 8 18 12 4 3
Transcribed Image Text:The functions f and g are continuous and differentiable for all values of x. The continuous function h(x) is given by h(x) = f(g(x)) — x². The table at the right gives values of f(x), ƒ'(x), g(x), and g'(x) at selected values of x. f(x) f'(x) g(x) 2 38 0 6 -3 a. Explain why there must be a value x for 2 < x < 8 such that h(x) = 0. b. Show that there must be an x = c, 4 < c < 6, such that h'(c) = 0. 4 12 9 8 6 9 -5 2 6 8 18 12 4 3
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