Your job is to find some shortcuts for taking derivatives. For example, if the function is of the form y = c, where c is a constant, then you know the graph is a horizontal line, with a slope of zero, and you don't have to even go through the limit gyrations to get the derivative. Do some experimenting with the limit definition on some easy functions to see what you get. When you post a shortcut, you must also post a good portion of the algebraic (or geometric) argument that supports it. No numerical or graphical (calculator) approximations will count as justification — you need to argue with algebra or geometry.

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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Your job is to find some shortcuts for taking derivatives. For example, if the function is of the form y = c, where c is a constant, then you know the graph is a horizontal line, with a slope of zero, and you don't have to even go through the limit gyrations to get the derivative.

Do some experimenting with the limit definition on some easy functions to see what you get. When you post a shortcut, you must also post a good portion of the algebraic (or geometric) argument that supports it. No numerical or graphical (calculator) approximations will count as justification — you need to argue with algebra or geometry.

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