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Question

If f"(x) > 0 x ϵ R then for any two real numbers x1 and x2 , (x1 x2)

A
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Solution

The correct option is B
Let A = (x1,f(x1)) and B = (x2,f(x2)) be any two points on the graph of y = f(x).
Since f"(x) > 0, in the graph of the function tangent will always lie below the curve. Hence chord AB will lie completely above the graph of y = f(x).
Hence f(x1)+f(x2)2>f(x1+x22)

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