Let F(x) =x2 a)Estimate the values of f'(0),f'(1/2) ,f'(1) , and f'(2) byusing a graphing device to zoom in on the graph of f.(b) Use symmetry to deduce the values of f'(1/2) , f'(-1) ,and f'(-2).(c) Use the results from parts (a) and (b) to guess a formulafor f'(x) .(d) Use the definition of a derivative to prove that yourguess in part (c) is correct.
Let F(x) =x2 a)Estimate the values of f'(0),f'(1/2) ,f'(1) , and f'(2) byusing a graphing device to zoom in on the graph of f.(b) Use symmetry to deduce the values of f'(1/2) , f'(-1) ,and f'(-2).(c) Use the results from parts (a) and (b) to guess a formulafor f'(x) .(d) Use the definition of a derivative to prove that yourguess in part (c) is correct.
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) =x2
a)Estimate the values of f'(0),f'(1/2) ,f'(1) , and f'(2) by
using a graphing device to zoom in on the graph of f.
(b) Use symmetry to deduce the values of f'(1/2) , f'(-1) ,
and f'(-2).
(c) Use the results from parts (a) and (b) to guess a formula
for f'(x) .
(d) Use the definition of a derivative to prove that your
guess in part (c) is correct.
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