63. GU Sketch the graph of f(x) = x/2 on [0, 6]. (a) Use the sketch to justify the inequalities for h > 0: f (4) – f(4 – h) f (4+h) – f(4) < f'(4) < (b) Use (a) to compute f'(4) to four decimal places. (c) Use a graphing utility to plot y = f(x) and the tangent line at x = 4, utilizing your estimate for f'(4).

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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63. GU Sketch the graph of f(x) = x/2 on [0, 6].
(a) Use the sketch to justify the inequalities for h > 0:
f (4) – f(4 – h)
f (4+h) – f(4)
< f'(4) <
(b) Use (a) to compute f'(4) to four decimal places.
(c) Use a graphing utility to plot y = f(x) and the tangent line at x = 4, utilizing your estimate for f'(4).
Transcribed Image Text:63. GU Sketch the graph of f(x) = x/2 on [0, 6]. (a) Use the sketch to justify the inequalities for h > 0: f (4) – f(4 – h) f (4+h) – f(4) < f'(4) < (b) Use (a) to compute f'(4) to four decimal places. (c) Use a graphing utility to plot y = f(x) and the tangent line at x = 4, utilizing your estimate for f'(4).
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