Given f(x) = x² - x - 6 for values of x = [0, 6], a. Write an equation of the line tangent to fat x = 4. b. If g(x) = [f(x)]², write an equation of any horizontal tangent lines to g.
Given f(x) = x² - x - 6 for values of x = [0, 6], a. Write an equation of the line tangent to fat x = 4. b. If g(x) = [f(x)]², write an equation of any horizontal tangent lines to g.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem Statement:**
Given \( f(x) = x^2 - x - 6 \) for values of \( x \in [0, 6] \),
a. Write an equation of the line tangent to \( f \) at \( x = 4 \).
b. If \( g(x) = [f(x)]^2 \), write an equation of any horizontal tangent lines to \( g \). Show how you arrive at your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc6ffa477-99d7-4e93-b7f8-2eced087179b%2F79b0680d-030e-455f-9374-46114971d2ad%2Fauwx4ig_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Given \( f(x) = x^2 - x - 6 \) for values of \( x \in [0, 6] \),
a. Write an equation of the line tangent to \( f \) at \( x = 4 \).
b. If \( g(x) = [f(x)]^2 \), write an equation of any horizontal tangent lines to \( g \). Show how you arrive at your answer.
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