Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Review - Concept Check: 14

Answer

The definition is $$f''(t)=\lim_{h\to0}\frac{f'(t+h)-f'(t)}{h}.$$ If $f(t)$ is the position function then $f''(t)$ is interpreted as the acceleration.

Work Step by Step

The second derivative of the function $f$ is the derivative of the derivative of the function $f$. This means that if the derivative is $f'(t)$ then the second derivative is $$f''(t)=\lim_{h\to0}\frac{f'(t+h)-f'(t)}{h}.$$ If $f(t)$ is the position function, then $f'(t)$ is instantaneous velocity and thus $f''(t)$ represents the instantaneous change of the velocity i.e. the acceleration.
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