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Question

Let f(x)={|x1|+a,x12x+3,x>1 If f(x) has local minimum at x=1 and a5 then a is equal to

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Solution

iff(x)hasalocalminimumatx=1thatmeansthatf(x)iscontinuousfunctionatx=1.so|x1|+a=2x+3(atx=1)a=2+3a=5

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