Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.2 Exercises: 75


The horizontal line is the derivative ($x=2=f'(x)$) and the sloping line is the original function ($f(x)=2x-2$)

Work Step by Step

The derivative is the rate of change so by checking which line represents the rate of change we can deduce the parent function and the derivative. The horizontal line represents a constant rate of change while the sloping line represents a variable rate of change; since the sloping line has a constant slope it makes sense for the horizontal line to represent its slope. It isn't possible for the sloping line to be the derivative of the horizontal line since the horizontal has a zero rate of change.
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