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9 8- 7 16 1 A 3 يها 2 1 If f(x) f'(3) = = g(x) g(x) h(x)' 2 3 x-values then 5 4 يها 2 1 h(x) 1 2 3 x-values

9 8- 7 16 1 A 3 يها 2 1 If f(x) f'(3) = = g(x) g(x) h(x)' 2 3 x-values then 5 4 يها 2 1 h(x) 1 2 3 x-values

Calculus: Early Transcendentals
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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The image displays two graphs and a mathematical expression. **Graph on the Left:** - Title: \( g(x) \) - Axes: X-axis labeled "x-values" (in red), Y-axis labeled "y-values" (in red) - Plot: A downward sloping line from point (0, 9) to point (5, 4). **Graph on the Right:** - Title: \( h(x) \) - Axes: X-axis labeled "x-values" (in red), Y-axis labeled "y-values" (in red) - Plot: An upward line from point (1, 1) to point (2.5, 5), and then downward from point (2.5, 5) to point (4, 1). **Text Below the Graphs:** "If \( f(x) = \frac{g(x)}{h(x)} \), then \( f'(3) = \) [blank box for answer]." These diagrams illustrate functions \( g(x) \) and \( h(x) \), showing their respective values for given x-values. The task involves calculating the derivative \( f'(3) \) based on the quotient of these two functions at \( x=3 \).
Transcribed Image Text:The image displays two graphs and a mathematical expression. **Graph on the Left:** - Title: \( g(x) \) - Axes: X-axis labeled "x-values" (in red), Y-axis labeled "y-values" (in red) - Plot: A downward sloping line from point (0, 9) to point (5, 4). **Graph on the Right:** - Title: \( h(x) \) - Axes: X-axis labeled "x-values" (in red), Y-axis labeled "y-values" (in red) - Plot: An upward line from point (1, 1) to point (2.5, 5), and then downward from point (2.5, 5) to point (4, 1). **Text Below the Graphs:** "If \( f(x) = \frac{g(x)}{h(x)} \), then \( f'(3) = \) [blank box for answer]." These diagrams illustrate functions \( g(x) \) and \( h(x) \), showing their respective values for given x-values. The task involves calculating the derivative \( f'(3) \) based on the quotient of these two functions at \( x=3 \).
Expert Solution
Step 1

Given that graph of gx and hx    and fx=gxhxTo find :f'3Solution :fx=gxhxf'x=g'xhx-h'xgxhx2f'3=g'3h3-h'3g3h32g'3=slope of gx at x=3h'3=slope of hx at x=3

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