See the attached picture. The functions f and g are continuous anddifferentiable for all values of x. Thecontinuous function h(x) is given byh(x) = f(g(x)) — x². The table at the rightgives values of f(x), ƒ'(x), g(x), and g'(x) atselected values of x.f(x)f'(x)g(x)23806-3a. 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) = 0.4129869-5268181243

Using the intermediate value theorem, it can be written that if f(a)>0, f(b)<0, then there…

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

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.

Chapter4: Calculating The Derivative

Section4.CR: Chapter 4 Review

Problem 5CR: Determine whether each of the following statements is true or false, and explain why. The chain rule...

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