Part 2 Let f be the continuous function defined on [-1,8] whose graph, consisting of two line segments, is shown at the right. Let g and h be the functions defined by g(x)=x²-x+3 and h(x) = 5e* - 9 sinx. A. The function k is defined by k(x) = f(x)g(x). Find k'(x) and evaluate when x = 1 B. The function m is defined by m(x) = f(x) Find m'(x) and g(x) evaluate when x = 0 C. Find h'(x) and evaluate when x = 2π. D. Find the value of x for 2 < x < 8 such that f'(x) = g'(x) -6- 4. 2 10 2 4 Graph of f 6 8
Part 2 Let f be the continuous function defined on [-1,8] whose graph, consisting of two line segments, is shown at the right. Let g and h be the functions defined by g(x)=x²-x+3 and h(x) = 5e* - 9 sinx. A. The function k is defined by k(x) = f(x)g(x). Find k'(x) and evaluate when x = 1 B. The function m is defined by m(x) = f(x) Find m'(x) and g(x) evaluate when x = 0 C. Find h'(x) and evaluate when x = 2π. D. Find the value of x for 2 < x < 8 such that f'(x) = g'(x) -6- 4. 2 10 2 4 Graph of f 6 8
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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Question
![**Part 2**
Let \( f \) be the continuous function defined on \([-1, 8]\) whose graph, consisting of two line segments, is shown at the right. Let \( g \) and \( h \) be the functions defined by \( g(x) = x^2 - x + 3 \) and \( h(x) = 5e^x - 9 \sin x \).
**A.** The function \( k \) is defined by \( k(x) = f(x)g(x) \). Find \( k'(x) \) and evaluate when \( x = 1 \).
**B.** The function \( m \) is defined by \( m(x) = \frac{f(x)}{g(x)} \). Find \( m'(x) \) and evaluate when \( x = 0 \).
**C.** Find \( h'(x) \) and evaluate when \( x = 2\pi \).
**D.** Find the value of \( x \) for \( 2 < x < 8 \) such that \( f'(x) = g'(x) \).
**Graph Description:**
The graph of \( f \) shows two line segments. The first segment extends from the point (0, 2) to approximately (3, 7), and the second segment descends from approximately (3, 7) to (8, approximately 2.5). The y-axis ranges from 0 to 8, and the x-axis from 0 to 8, displaying the linear changes of the function \( f \) over the defined interval.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F981166fe-4516-4e5d-91f3-95cacb37d8bb%2F881ec300-2311-4f67-8e81-61a9d457cd86%2F6fh13v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Part 2**
Let \( f \) be the continuous function defined on \([-1, 8]\) whose graph, consisting of two line segments, is shown at the right. Let \( g \) and \( h \) be the functions defined by \( g(x) = x^2 - x + 3 \) and \( h(x) = 5e^x - 9 \sin x \).
**A.** The function \( k \) is defined by \( k(x) = f(x)g(x) \). Find \( k'(x) \) and evaluate when \( x = 1 \).
**B.** The function \( m \) is defined by \( m(x) = \frac{f(x)}{g(x)} \). Find \( m'(x) \) and evaluate when \( x = 0 \).
**C.** Find \( h'(x) \) and evaluate when \( x = 2\pi \).
**D.** Find the value of \( x \) for \( 2 < x < 8 \) such that \( f'(x) = g'(x) \).
**Graph Description:**
The graph of \( f \) shows two line segments. The first segment extends from the point (0, 2) to approximately (3, 7), and the second segment descends from approximately (3, 7) to (8, approximately 2.5). The y-axis ranges from 0 to 8, and the x-axis from 0 to 8, displaying the linear changes of the function \( f \) over the defined interval.
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