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
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
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)
Transcribed Image Text: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.
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faca5ab5d-d1b4-4091-b3ec-a6eaf8cb8003%2F8521cd90-f1bd-413e-8e5a-9820317078ac%2Fbtc8gcw_processed.jpeg&w=3840&q=75)
