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For a double diferentiable function f...

For a double diferentiable function f(x) if `f''(x) ge 0` then f(x) is concave upward and if `f''(x) le 0` then f(x) is concave downward

if f(x) is a concave upward in [a,b] and `alpha , beta in [a,b]` the `(k_(1)(alpha)+k_(2)f(beta))/(k_(1)+k_(2)) ge f((k_(1) alpha +k_(2)beta)/(k_(1)+k_(2)))` where `K_(1)+K_(2) in R`
if f(x) is a concave downward in `[a,b] " and "alpha, beta in [a,b] " then "(k_(1)(alpha)+k_(2)f(beta))/(k_(1)+k_(2)) le f((k_(1) alpha +k_(2)beta)/(k_(1)+k_(2)))` where `k_(1)+k_(2) in R`
then answer the following :
Which of the following is true

A

`A gt B`

B

`A lt B`

C

A=B

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
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