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Differential Calculus

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 Joined: 4 Apr 2007 Post: 29
3 May 2007 11:29:53 IST
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aieee question
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Differential Calculus

f(x)=min{x+1,|x|+1}
is the function diff at x=1?

if no plz explain fully

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Joined: 1 Dec 2006
Posts: 2108
3 May 2007 11:52:04 IST
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it is differntiable at x= 1
just see the attached figure ...it will be the graph of the two functions...
frm this the minimum value will be always x+1

thus it will be differentiable at x=1

New kid on the Block

Joined: 4 Apr 2007
Posts: 29
4 May 2007 23:14:31 IST
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wl i also thnk so but fiit jee website key says something else

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Joined: 23 Jan 2007
Posts: 7958
8 May 2007 16:24:56 IST
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Since x <= |x|

x+1 <= |x|+1

Hence min(x+1,|x|+1) = x+1

Hence the curve is a straight line : y = x + 1 which is differentiable everywhere.

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