Let f(x) = x 2 + 4x − 2. (a) Find the slope of the secant lines from (1,3) through (x, f(x)) for x = 1.1, 1.01, 1.001 and 1.0001. (b) Use the answers from (a) to estimate the value of the slope of the tangent line at (1, 3). (c) Use the shortcut methods for taking derivatives to find f 0 (x). (d) Use your derivative to find the slope of the tangent line at (1, 3). (e) Find the equation of the tangent line to f at (1, 3). Plot both the tangent line and the function on the same graph.
Let f(x) = x 2 + 4x − 2. (a) Find the slope of the secant lines from (1,3) through (x, f(x)) for x = 1.1, 1.01, 1.001 and 1.0001. (b) Use the answers from (a) to estimate the value of the slope of the tangent line at (1, 3). (c) Use the shortcut methods for taking derivatives to find f 0 (x). (d) Use your derivative to find the slope of the tangent line at (1, 3). (e) Find the equation of the tangent line to f at (1, 3). Plot both the tangent line and the function on the same graph.
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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Let f(x) = x 2 + 4x − 2.
(a) Find the slope of the secant lines from (1,3) through (x, f(x)) for x = 1.1, 1.01, 1.001 and 1.0001.
(b) Use the answers from (a) to estimate the value of the slope of the tangent line at (1, 3).
(c) Use the shortcut methods for taking derivatives to find f 0 (x).
(d) Use your derivative to find the slope of the tangent line at (1, 3).
(e) Find the equation of the tangent line to f at (1, 3). Plot both the tangent line and the function on the same graph.
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