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Let f:R rarr R, y=f(x), f(0)=0, f'(x) gt...

Let `f:R rarr R, y=f(x), f(0)=0, f'(x) gt0 and f''(x)gt0`. Three point `A(alpha, f(alpha)), B(beta,f(beta)), C(gamma, f(gamma)) on y=f(x)` such that `0lt alpha lt beta lt gamma.`
Which of the following is true?

A

`gammaf(gamma+beta-alpha)gt (gamma+beta-alpha)f(gamma)`

B

gammaf(gamma+beta-alpha)lt (gamma+beta-alpha)f(gamma)`

C

`alphaf(gamma+beta-alpha)gt (gamma+beta-alpha)f(alpha)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
As `gamma+beta-alpha gt gamma`
`f(gamma+beta-alpha)/(gamma+beta-alpha)gt(f(gamma))/(gamma)`
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