CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Let fx=ax2+3,x>1x+52,x1 . If f(x) is differentiable at x = 1, then a = ____________.


Solution


The given function fx=ax2+3,x>1x+52,x1 is differentiable at x = 1.

Lf'1=Rf'1

limh0f1-h-f1-h=limh0f1+h-f1h

limh01-h+52-1+52-h=limh0a1+h2+3-1+52h

limh0-h-h=limh0a1+h2-12h

1=limh0a-12+a2h+h2h

1=limh0a-12+ah2+hh

1=limh0a-12h+limh0a2+h

Here, LHS is finite.

So, for RHS to be finite, we must have

a-12=0

a=12

Thus, the value of a is 12.


Let fx=ax2+3,x>1x+52,x1 . If f(x) is differentiable at x = 1, then a =      12     .

Mathematics
RD Sharma XII Vol 1 (2019)
All

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
Same exercise questions
View More


similar_icon
People also searched for
View More



footer-image