Estimate the derivative from the table of average rates of change. HINT [See discussion at the beginning of the section.] (Round your answer to one decimal place.)r'(6) = h10.10.010.0010.0001Ave. Rate ofChange of r Over[6, 6 + h]-1.7-1.53-1.511-1.50052-1.5000038h-1-0.1-0.01-0.001-0.0001Ave. Rate ofChange of r Over[6 + h, 6]0.0-1.45-1.466-1.49914-1.4999969

The objective is to find r'(6) from the given table. On the interval (6,6+h];On the interval [6-h,6); All the points look like Therefore at x=6, the limit value is -1.5 Hence, y(6)=r'(6)=-1.5.

Answered: Estimate the derivative from the table…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Estimate the derivative from the table of average rates of change. HINT [See discussion at the beginning of the section.] (Round your answer to one decimal place.)

r'(6)

h	1	0.1	0.01	0.001	0.0001
Ave. Rate of Change of r Over [ 6, 6 + h]	-1.7	-1.53	-1.511	-1.50052	-1.5000038
h	-1	-0.1	-0.01	-0.001	-0.0001
Ave. Rate of Change of r Over [6 + h, 6]	0.0	-1.45	-1.466	-1.49914	-1.4999969