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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Question

Transcribed Image Text:**Problem Statement:**
Given that \( h(x) = 2g(x) \), what is \( h'(6) \)?
**Graph Description:**
The graph consists of two line segments representing functions \( g(x) \) and \( f(x) \).
- **Function \( g(x) \):** This is shown as a blue dashed line. It starts at the point (0, 1), rises to (2, 4), and then declines to (6, 2).
- **Function \( f(x) \):** This appears as a red solid line. It starts at (0, 6), falls sharply to (2, -1), and then rises steadily upward past (6, 3).
**Options for \( h'(6) \):**
- \( 6 \)
- \( -1/2 \)
- \( 18 \)
- \( -6 \)
- \( 1/2 \)
**Instructions:**
To find \( h'(6) \), determine the derivative of the function \( g(x) \) at \( x = 6 \) and then multiply it by 2, as \( h(x) = 2g(x) \). Analyze the slope of the blue dashed line between \( x=3 \) and \( x=6 \) to find \( g'(6) \), and apply the result to find \( h'(6) \).
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