0

Guest

Courses New

the function f(x) = jx??2j x2 is unde ned at x = 0 and jx??2j changes sign at x = 2 hence we divide the domain of f(x) in to three intervals (??1; 0) (0; 2) (2;1) f(x) = 8> >: 2??x x2 x 2 (??1; 0) 2??x x2 x 2 (0; 2) x??2 x2 x 2 (2;1) nd the derivative for each of these intervals f0(x) = 8> >: x2??4x x4 x 2 (??1; 0) x2??4x x4 x 2 (0; 2) 4x??x2 x4 x 2 (2;1) . As x4 is always positive determine the sign of numerator in each and hence nd the intervals of mono- tonicity. Increasing in (??1; 0) [ (4;1) Decreasing in (0; 2) [ (2; 4).

the function f(x) = jx??2j
x2 is unde ned at x = 0 and jx??2j changes sign at x = 2 hence we divide the domain
of f(x) in to three intervals (??1; 0) (0; 2) (2;1)
f(x) =
8><
>:
2??x
x2 x 2 (??1; 0)
2??x
x2 x 2 (0; 2)
x??2
x2 x 2 (2;1)
nd the derivative for each of these intervals f0(x) =
8><
>:
x2??4x
x4 x 2 (??1; 0)
x2??4x
x4 x 2 (0; 2)
4x??x2
x4 x 2 (2;1)
.
As x4 is always positive determine the sign of numerator in each and hence nd the intervals of mono-
tonicity.
Increasing in (??1; 0) [ (4;1)
Decreasing in (0; 2) [ (2; 4).

Grade:12

1 Answers

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
10 years ago
175-1573_Untitled.jpg

Sher Mohammad
B.Tech, IIT Delhi.

Think You Can Provide A Better Answer ?

Other Related Questions on Integral Calculus

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More