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

Find the derivatives of each of the absolute value and piecewise-defined functions in Exercises 65-72.

f(x)=x3,ifx<1x,ifx1

Short Answer

Expert verified

The derivative of the function isf'(x)=3x2,ifx<1DNE,ifx=11,ifx>1.

Step by step solution

01

Step 1. Given Information

The given function isf(x)=x3,ifx<1x,ifx1.

02

Step 2. Find the derivative

  • It is known that, the power rule of derivative is (xn)'=nxn-1.
  • Find the derivative for x<1.

f'(x)=ddx(x3)=3x2

  • Find the derivative for x>1.

f'(x)=ddx(x)=1

  • Since 3(1)21, the derivatives at left and right pieces are not equal at x=1. The derivative does not exists at x=1.
  • So, the derivative of the function is, f'(x)=3x2,ifx<1DNE,ifx=11,ifx>1.

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