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Use the figure below to calculate the derivative, g' (5) if g(x) = ƒ¯| (x). (2.1,5.5) S(x) (2 ,5 ) Enter the exact answer. g'(5) = |

Use the figure below to calculate the derivative, g' (5) if g(x) = ƒ¯| (x). (2.1,5.5) S(x) (2 ,5 ) Enter the exact answer. g'(5) = |

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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how to calculate points from tangent line to insert function with the slope value

**Calculating the Derivative of an Inverse Function** To solve for the derivative \( g'(5) \) where \( g(x) = f^{-1}(x) \), use the figure below which depicts the function \( f(x) \). **Points on the Graph:** - The curve \( f(x) \) is shown with two labeled points: - \( (2, 5) \) - \( (2.1, 5.5) \) **Graph Explanation:** - The curve represents the function \( f \). - The points \( (2, 5) \) and \( (2.1, 5.5) \) indicate that when \( x = 2 \), \( f(x) = 5 \), and at \( x = 2.1 \), \( f(x) = 5.5 \). **Task:** - Use the information from the graph to find \( g'(5) \). Since \( g(x) = f^{-1}(x) \), and by the differentiation rule for inverse functions, the derivative \( g'(a) \) is \( \frac{1}{f'(b)} \) where \( f(b) = a \). **Enter the Exact Answer:** - Calculate \( g'(5) \) using the provided points and the slope of \( f(x) \).
Transcribed Image Text:**Calculating the Derivative of an Inverse Function** To solve for the derivative \( g'(5) \) where \( g(x) = f^{-1}(x) \), use the figure below which depicts the function \( f(x) \). **Points on the Graph:** - The curve \( f(x) \) is shown with two labeled points: - \( (2, 5) \) - \( (2.1, 5.5) \) **Graph Explanation:** - The curve represents the function \( f \). - The points \( (2, 5) \) and \( (2.1, 5.5) \) indicate that when \( x = 2 \), \( f(x) = 5 \), and at \( x = 2.1 \), \( f(x) = 5.5 \). **Task:** - Use the information from the graph to find \( g'(5) \). Since \( g(x) = f^{-1}(x) \), and by the differentiation rule for inverse functions, the derivative \( g'(a) \) is \( \frac{1}{f'(b)} \) where \( f(b) = a \). **Enter the Exact Answer:** - Calculate \( g'(5) \) using the provided points and the slope of \( f(x) \).
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