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Take the function: f (x) = arctan(x") (a) Give a formula for the average rate of change of f(x) over the interval [1,1+ h]. (b) Substitute a number of different values into h to estimate the limit of the average rate of change as h approaches 0 from the left. (c) Substitute a number of different values into h to estimate the limit of the average rate of change as h approaches 0 from the right. (d) Using the previous two parts, does it look like the derivative f'(1) exists? If so, give an estimate for the value of f'(1).

Take the function: f (x) = arctan(x") (a) Give a formula for the average rate of change of f(x) over the interval [1,1+ h]. (b) Substitute a number of different values into h to estimate the limit of the average rate of change as h approaches 0 from the left. (c) Substitute a number of different values into h to estimate the limit of the average rate of change as h approaches 0 from the right. (d) Using the previous two parts, does it look like the derivative f'(1) exists? If so, give an estimate for the value of f'(1).

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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Take the function: f (x) = arctan(x") (a) Give a formula for the average rate of change of f(x) over the interval [1,1+ h]. (b) Substitute a number of different values into h to estimate the limit of the average rate of change as h approaches 0 from the left. (c) Substitute a number of different values into h to estimate the limit of the average rate of change as h approaches 0 from the right. (d) Using the previous two parts, does it look like the derivative f'(1) exists? If so, give an estimate for the value of f'(1).
Transcribed Image Text:Take the function: f (x) = arctan(x") (a) Give a formula for the average rate of change of f(x) over the interval [1,1+ h]. (b) Substitute a number of different values into h to estimate the limit of the average rate of change as h approaches 0 from the left. (c) Substitute a number of different values into h to estimate the limit of the average rate of change as h approaches 0 from the right. (d) Using the previous two parts, does it look like the derivative f'(1) exists? If so, give an estimate for the value of f'(1).
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