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f(x) g(x) XX 2 5 6 7 The graphs of the functions f and g are shown below. If h(x) = Y A Provide your answer below: h'(3) = 7 6 5 4+ 3 2 1 find h' (3).. X

f(x) g(x) XX 2 5 6 7 The graphs of the functions f and g are shown below. If h(x) = Y A Provide your answer below: h'(3) = 7 6 5 4+ 3 2 1 find h' (3).. X

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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### Problem Statement The graphs of the functions \( f \) and \( g \) are shown below. If \( h(x) = \frac{f(x)}{g(x)} \), find \( h'(3) \). ### Graph Description The graph displays two functions, \( f \) (in blue) and \( g \) (in red), plotted on a coordinate system with the horizontal axis labeled \( x \) and the vertical axis labeled \( y \). - The \( x \)-axis ranges from \( -1 \) to \( 7 \). - The \( y \)-axis ranges from \( -1 \) to \( 7 \). #### Function \( f \) (Blue Line) - For \( x \) values from \( 0 \) to \( 1 \), \( f(x) \) decreases from \( 6 \) to \( 2 \). - For \( x \) values from \( 1 \) to \( 2 \), \( f(x) \) increases from \( 2 \) to \( 5 \). - For \( x \) values from \( 2 \) to \( 4 \), \( f(x) \) decreases from \( 5 \) to \( 0 \). - For \( x \) values from \( 4 \) to \( 6 \), \( f(x) \) increases from \( 0 \) to \( 6 \). #### Function \( g \) (Red Line) - For \( x \) values from \( 0 \) to \( 2 \), \( g(x) \) increases from \( 1 \) to \( 5 \). - For \( x \) values from \( 2 \) to \( 3 \), \( g(x) \) decreases from \( 5 \) to \( 2 \). - For \( x \) values from \( 3 \) to \( 4 \), \( g(x) \) decreases from \( 2 \) to \( 1 \). - For \( x \) values from \( 4 \) to \( 6 \), \( g(x) \) increases from \( 1 \) to \( 6 \). ### Task Provide your answer below: \[ h'(3) = \boxed{} \] To find \( h'(3) \), we will use the quotient rule for differentiation.
Transcribed Image Text:### Problem Statement The graphs of the functions \( f \) and \( g \) are shown below. If \( h(x) = \frac{f(x)}{g(x)} \), find \( h'(3) \). ### Graph Description The graph displays two functions, \( f \) (in blue) and \( g \) (in red), plotted on a coordinate system with the horizontal axis labeled \( x \) and the vertical axis labeled \( y \). - The \( x \)-axis ranges from \( -1 \) to \( 7 \). - The \( y \)-axis ranges from \( -1 \) to \( 7 \). #### Function \( f \) (Blue Line) - For \( x \) values from \( 0 \) to \( 1 \), \( f(x) \) decreases from \( 6 \) to \( 2 \). - For \( x \) values from \( 1 \) to \( 2 \), \( f(x) \) increases from \( 2 \) to \( 5 \). - For \( x \) values from \( 2 \) to \( 4 \), \( f(x) \) decreases from \( 5 \) to \( 0 \). - For \( x \) values from \( 4 \) to \( 6 \), \( f(x) \) increases from \( 0 \) to \( 6 \). #### Function \( g \) (Red Line) - For \( x \) values from \( 0 \) to \( 2 \), \( g(x) \) increases from \( 1 \) to \( 5 \). - For \( x \) values from \( 2 \) to \( 3 \), \( g(x) \) decreases from \( 5 \) to \( 2 \). - For \( x \) values from \( 3 \) to \( 4 \), \( g(x) \) decreases from \( 2 \) to \( 1 \). - For \( x \) values from \( 4 \) to \( 6 \), \( g(x) \) increases from \( 1 \) to \( 6 \). ### Task Provide your answer below: \[ h'(3) = \boxed{} \] To find \( h'(3) \), we will use the quotient rule for differentiation.
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