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If `f(x)` is a differentiable function satisfying `f^(')(x)lt2` for all `xepsilonR` and `f(1)=2,` then greatest possible integral value of `f(3)` is

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The correct Answer is:
5
`(f(3)-f(1))/(3-1)=f^(')(c),c 1ltclt3`
`f^(')=(f(3)-2)/2lt2`
`:'f(3)lt6`
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