If f"(x)>0∀xϵR then for any two real numbers x1andx2,(x1≠x2)
A
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B
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C
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D
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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)