The function f & g are differentiable everywhere except x=1 and x=4. The graph of g is given in the figure above and select the values of f & f’ are given in the table above. If h(x) = f(g(x)), find h’(3) The problem involves two functions, \( f \) and \( g \), which are differentiable everywhere except at \( x = 1 \) and \( x = 4 \). The task is to find \( h(3) \) where \( h(x) = f(g(x)) \).### Graph Analysis:The graph of \( g(x) \) is a piecewise linear function with the following points:- \( g(0) = 1 \)- \( g(1) = 0 \)- \( g(2) = 7 \)- \( g(3) = 4 \)- \( g(4) = 1 \)### Table of Values:A table provides selected values of \( f(x) \) and its derivative \( f'(x) \):\[\begin{array}{c|c|c}x & f(x) & f'(x) \\\hline-1 & 6 & 3 \\2 & -4 & 5 \\3 & 5 & 4 \\7 & -2 & 0 \\\end{array}\]### Solution Steps:1. Evaluate \( g(3) \) using the graph: \( g(3) = 4 \).2. Find \( f(g(3)) = f(4) \). Since \( f(4) \) is not directly given, note that \( f \) might need additional information.3. Check the table for \( f \) values around the calculated \( g(x) \), but unfortunately \( x = 4 \) is not available.Given options are for \( h(3) \):- **(A) -8**- **(B) -5**- **(C) 5**- **(D) 6**Assuming \( f \) values or additional context is provided externally, select from the above options.

Answered: Image /qna-images/answer/8521cd90-f1bd-413e-8e5a-9820317078ac.jpg

4 g(x) 3 N 2 1 2 3 -1 0 4 5 6 7 x f (x) f'(x) -1 3 6 2 -4 5 3 4 -2 7 0 1 9. The functions f and g are differentiable everywhere except at x = 1 and x = 4. The graph of gi figure above and selected values of f and f' are given in the table above. If h(x) = f(g(x)), find (A) - 8 (B) - 5 (C) 5 (D) 6

4 g(x) 3 N 2 1 2 3 -1 0 4 5 6 7 x f (x) f'(x) -1 3 6 2 -4 5 3 4 -2 7 0 1 9. The functions f and g are differentiable everywhere except at x = 1 and x = 4. The graph of gi figure above and selected values of f and f' are given in the table above. If h(x) = f(g(x)), find (A) - 8 (B) - 5 (C) 5 (D) 6

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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