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: 76

Answer

The sloping line is the derivative ($f'(x)$) while the parabola is the parent function ($f(x)$).

Work Step by Step

The equation of a parabola is $y=ax^2+bx+c$ and the derivative of the general equation of a parabola is $y'=2ax+b$ hence the parabola is the parent function while the sloping line is the derivative. Furthermore, the derivative of the general equation of a sloping line ($y=mx+b$ ) is $m$ hence the derivative of a sloping line would be a horizontal line of equation $y=m$; due to this, the sloping line cannot be the parent function.
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