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Examine the graph of f(x) = 2*. у 1 1 1 2 a. Use the graph to explain why, for h > 0, a+ h) - f(a) h f(a h) f(a) < f'(a) -h a. Because f(x) is Веcause h > 0, а — h is increasing the slope of the secant line through less than h, f(a - h)) and (a, f(a)) is the points (a the slope of the tangent line at the point (a, f(a)). less than Similarly, a h is a, so the slope of the secant line through the points (a, f(a)) and greater than (a h, f(ah)) is the slope of the tangent line at the point (a, f(a)). This explains the inequality greater than b. By choosing a small enough value for h, you can estimate f'(a) with arbitrary precision by computing the lower bound a h) -JaJ and the upper bOund (a + h) - J\_ and interpolating (finding the average of the two -h h bounds). To save time, observe that the average of the lower and upper bounds is f(ah) f(a - h) 2h Use the method described with h = 0.000001 to estimate f'(0) to four decimal places. Give your answer using decimal notation f'(0) c. Use the same method with h = 0.000001 to estimate f'(1), f'(2), and f'(3). Use decimal notation and give your answers to four decimal places f'(1) f'(2) f(3)

Examine the graph of f(x) = 2*. у 1 1 1 2 a. Use the graph to explain why, for h > 0, a+ h) - f(a) h f(a h) f(a) < f'(a) -h a. Because f(x) is Веcause h > 0, а — h is increasing the slope of the secant line through less than h, f(a - h)) and (a, f(a)) is the points (a the slope of the tangent line at the point (a, f(a)). less than Similarly, a h is a, so the slope of the secant line through the points (a, f(a)) and greater than (a h, f(ah)) is the slope of the tangent line at the point (a, f(a)). This explains the inequality greater than b. By choosing a small enough value for h, you can estimate f'(a) with arbitrary precision by computing the lower bound a h) -JaJ and the upper bOund (a + h) - J\_ and interpolating (finding the average of the two -h h bounds). To save time, observe that the average of the lower and upper bounds is f(ah) f(a - h) 2h Use the method described with h = 0.000001 to estimate f'(0) to four decimal places. Give your answer using decimal notation f'(0) c. Use the same method with h = 0.000001 to estimate f'(1), f'(2), and f'(3). Use decimal notation and give your answers to four decimal places f'(1) f'(2) f(3)

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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Examine the graph of f(x) = 2*. у 1 1 1 2 a. Use the graph to explain why, for h > 0, a+ h) - f(a) h f(a h) f(a) < f'(a) -h a. Because f(x) is Веcause h > 0, а — h is increasing the slope of the secant line through less than h, f(a - h)) and (a, f(a)) is the points (a the slope of the tangent line at the point (a, f(a)). less than Similarly, a h is a, so the slope of the secant line through the points (a, f(a)) and greater than (a h, f(ah)) is the slope of the tangent line at the point (a, f(a)). This explains the inequality greater than b. By choosing a small enough value for h, you can estimate f'(a) with arbitrary precision by computing the lower bound a h) -JaJ and the upper bOund (a + h) - J\_ and interpolating (finding the average of the two -h h bounds). To save time, observe that the average of the lower and upper bounds is f(ah) f(a - h) 2h Use the method described with h = 0.000001 to estimate f'(0) to four decimal places. Give your answer using decimal notation f'(0) c. Use the same method with h = 0.000001 to estimate f'(1), f'(2), and f'(3). Use decimal notation and give your answers to four decimal places f'(1) f'(2) f(3)
Transcribed Image Text:Examine the graph of f(x) = 2*. у 1 1 1 2 a. Use the graph to explain why, for h > 0, a+ h) - f(a) h f(a h) f(a) < f'(a) -h a. Because f(x) is Веcause h > 0, а — h is increasing the slope of the secant line through less than h, f(a - h)) and (a, f(a)) is the points (a the slope of the tangent line at the point (a, f(a)). less than Similarly, a h is a, so the slope of the secant line through the points (a, f(a)) and greater than (a h, f(ah)) is the slope of the tangent line at the point (a, f(a)). This explains the inequality greater than b. By choosing a small enough value for h, you can estimate f'(a) with arbitrary precision by computing the lower bound a h) -JaJ and the upper bOund (a + h) - J\_ and interpolating (finding the average of the two -h h bounds). To save time, observe that the average of the lower and upper bounds is f(ah) f(a - h) 2h Use the method described with h = 0.000001 to estimate f'(0) to four decimal places. Give your answer using decimal notation f'(0) c. Use the same method with h = 0.000001 to estimate f'(1), f'(2), and f'(3). Use decimal notation and give your answers to four decimal places f'(1) f'(2) f(3)
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