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

Suppose f is a piecewise-defined function, equal to g(x) if x < 2 and h(x) if x ≥ 2, where g and h are continuous and differentiable everywhere. If g(2) = h(2), is the function f necessarily differentiable at x = 2? Why or why not?

Short Answer

Expert verified

Thefunctioniscontinuousatx=2butnotdifferentiableatx=2.

Step by step solution

01

Step 1. Given information is:

f(x)=g(x),ifx<2h(x),ifx2andg(2)=h(2)

02

Step 2. Result

Sinceg(2)=h(2)itmeansthatthefunctioniscontinuousatx=2butitisnotnecessarythatitisdifferentiableatx=2.Forthis,followingexamplecanbetaken:f(x)=2x+3,ifx<2x2+3,ifx2Hence,thefunctioniscontinuousatx=2butnotdifferentiableatx=2.

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