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If f(x)={{:(3-x^(2)",",xle2),(sqrt(a+14)...

If `f(x)={{:(3-x^(2)",",xle2),(sqrt(a+14)-|x-48|",",xgt2):}` and if f(x) has a local maxima at x = 2, then greatest value of a is

A

2013

B

2012

C

2011

D

2010

Text Solution

Verified by Experts

The correct Answer is:
C
Local maximum at x = 2
`rArr" "underset(hrarr0)(lim)f(2+h)lef(2)`
`rArr" "underset(hrarr0)(lim)(sqrt(a+14)-|2+h-48|)le3-2^(2)`
`rArr" "sqrt(a+14)le45 rArr a le 2011`
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