Calculus: Early Transcendentals 8th Edition

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

Chapter 2 - Review - Concept Check: 11

Answer

The instantaneous velocity is given by $$v(t)=\lim_{h\to0}\frac{f(t+h)-f(t)}{h}.$$ It can be interpreted as the slope of the tangent line of the graph of $f$ at the point $(t,f(t))$.

Work Step by Step

The instantaneous velocity says how much the position changes per unit interval of time in the limit when the length of this interval tends to zero which is $$v(t)=\lim_{h\to0}\frac{f(t+h)-f(t)}{h}.$$ Here the length we divided the small change in position $f(t+h)-f(t)$ with the small time interval $h$. This expression matches the definition of the slope of the tangent line of the graph of $f$ at the point $(t,f(t))$ so in terms of the graph of $f$, we interpret the instantaneous velocity as the slope of the tangent.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.