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Question

If f(x)={|x2|+a,x23x1,x>2 has a local minimum at x=2, then a=

A
5
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B
4
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C
1
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D
2
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Solution

The correct option is A 5
f(x)={2+ax,x23x1,x>2
Left hand derivative of f(x) at x=2 is 1<0 and RHD =3>0. .
f(x) is decreasing in (,2] and increasing in (2,).
minimum value of f is =(3×21)=2+a2
a=5

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