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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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Appreciate help with all. Thanks in advance
**Question 4** If \( f \) and \( g \) are the functions whose graphs are shown, let \( h(x) = f(g(x)) \). Find \( h'(6) \). The graph provided shows two lines. The line representing \( f(x) \) is in red, and the line representing \( g(x) \) is in blue. The x-axis ranges from -2 to 6, and the y-axis ranges from -2 to 6. Key points where the functions cross the axes or each other are important for understanding the derivatives at specific points. **Question 5** Let \( y = 5^{6x^2 - x + 12} \). Find \( \frac{dy}{dx} \). *Enter your answer as an integer or an exact fraction.*
Transcribed Image Text:**Question 4** If \( f \) and \( g \) are the functions whose graphs are shown, let \( h(x) = f(g(x)) \). Find \( h'(6) \). The graph provided shows two lines. The line representing \( f(x) \) is in red, and the line representing \( g(x) \) is in blue. The x-axis ranges from -2 to 6, and the y-axis ranges from -2 to 6. Key points where the functions cross the axes or each other are important for understanding the derivatives at specific points. **Question 5** Let \( y = 5^{6x^2 - x + 12} \). Find \( \frac{dy}{dx} \). *Enter your answer as an integer or an exact fraction.*
**Question 9** If \( h(x) = \sqrt{3f(x) + 10} \), where \( f(1) = 5 \) and \( f'(1) = 5 \), find \( h'(1) \). Your answer should be an integer (like -2 or 3), a simplified proper fraction (like 2/3), or an improper fraction (like -3/2). [Blank space for answer]
Transcribed Image Text:**Question 9** If \( h(x) = \sqrt{3f(x) + 10} \), where \( f(1) = 5 \) and \( f'(1) = 5 \), find \( h'(1) \). Your answer should be an integer (like -2 or 3), a simplified proper fraction (like 2/3), or an improper fraction (like -3/2). [Blank space for answer]
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