Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Let lbe the line connecting two points (a,f(a))and (b,f(b))on the graph of a function f. What does this line lhave to do with the average rate of change of fon the interval [a,b],and why?

Short Answer

Expert verified

The line can be the tangent line of the function atx=c.

Step by step solution

01

Step 1. Given information

A function f(x).

A line l.

Two points(a,f(a)),(b,f(b)).

02

Step 2. Explanation

The average rate of change of the fat point x=ain the interval [a,b]will be :-

f(b)-f(a)b-a

If the intervals is very short, that means x=aand x=bare very close to each other , then f(b)-f(a)b-awill represent the slope of the tangent line at x=cand hence the line can be the tangent line of the function at x=c.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Study anywhere. Anytime. Across all devices.

Sign-up for free