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 1 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 1 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 1 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 1 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).
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter1: Functions
Section1.2: Functions Given By Tables
Problem 32SBE: Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it...
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