CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

f(x)={x2         x x0ax+b, x>x0. If f(x) is differentiable at x0. Then


  1. None of these


Solution

The correct option is D


For f(x) to be diffrentiable at x0 f(x) sould be continuous at x0 and LHD& RHD of f(x) at x0 should be

equal.

Therefore, limx x0=x20

limx x 0+=ax0+b

 x20=ax0+b.....(1)

LHD limxx0=(x0+h)2x20hlimx0=x20+2hx0+h2x2h

=limx 0=hh(2x0+h)=2x0

RHD,limh 0+=ah+bbh=alimh 0hh=a

 LHD=RHD a=2x0......(2)

Substituting (2) in (1)

x20=ax0+b

x20=2ax20+b

 b=x20.

 a=2x0,   b=x20

Answer option -b

flag
 Suggest corrections
thumbs-up
 
0 Upvotes


Similar questions
View More


People also searched for
View More



footer-image