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If f(x)gt0 and f"(x)gt0 forallx in R, th...

If `f(x)gt0 `and` f"(x)gt0 forallx in R,` then for any two real numbers `x_1` and `x_2,(x_1nex_2)`

A

`f((x_1+x_2)/2)gt(f(x_1)+f'(x_2))/2`

B

`f((x_1+x_2)/2)lt(f(x_1)+f(x_2))/2`

C

`f'((x_1+x_2)/2)gt(f'(x_1)+f'(x_2))/2`

D

`f'((x_1+x_2)/2)lt(f'(x_1)+f'(x_2))/2`

Text Solution

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The correct Answer is:
B
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