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Question

The minimum of f(x)=1+x+x21x+x2 occurs at x =

A
-1
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B
1
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C
2
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D
-2
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Solution

The correct option is B -1
f(x)=1+2x1x+x2
f1(x)=2(1x+x2)2x(2x1)(1x+x2)2
0=2x2+2(1x+x2)2
x=±1
f1(x)>0 If 1<x<1
f1(x)<0 If x>1 or x<1
So f(x) is min at x=1

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