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Consider the following function x² - 2x, if x < 0, f(x)= = -2x, if x > 0. 1. Show that f(x) is continuous at x = 0. 2. Use the limit definition of the derivative to compute f'(0). Hint: You will need to use directional limits.

Consider the following function x² - 2x, if x < 0, f(x)= = -2x, if x > 0. 1. Show that f(x) is continuous at x = 0. 2. Use the limit definition of the derivative to compute f'(0). Hint: You will need to use directional limits.

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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Consider the following function x² - 2x, if x < 0, f(x)= = -2x, if x > 0. 1. Show that f(x) is continuous at x = 0. 2. Use the limit definition of the derivative to compute f'(0). Hint: You will need to use directional limits.
Transcribed Image Text:Consider the following function x² - 2x, if x < 0, f(x)= = -2x, if x > 0. 1. Show that f(x) is continuous at x = 0. 2. Use the limit definition of the derivative to compute f'(0). Hint: You will need to use directional limits.
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