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$Let f : R \to R, f (0) = 0, f^{'} (x) > 0 and f^{''} (x) > 0 and A (α, f (α)), B (β, f (β)), C (γ, f (γ))$ $be three points on the graph of y = f (x) and$
$0 < α < β < γ . Then which of the following is true?$

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γ fγ+β−α>γ+β−αfγ

γ fγ+β−α<γ+β−αfγ

α fγ+β−α<γ+β−αfα

α fβ<βfα

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detailed solution

Correct option is A

f(x)x is an increasing function slope of OP= fx-f0x-0=fxx is increasing, where Px,fx∴f(γ+β−α)γ+β−α>f(γ)γ since β-α>0⇒γ+β-α>γ⇒γf(γ+β−α)>(γ+β−α)f(γ)

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Let f:R→R,f(0)=0,f′(x)>0 and f′′(x)>0 and Aα, fα, Bβ, fβ, Cγ, fγ be three points on the graph of y=f(x) and 0<α<β<γ . Then which of the following is true?

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Ready to Test Your Skills?

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$Let f : R \to R, f (0) = 0, f^{'} (x) > 0 and f^{''} (x) > 0 and A (α, f (α)), B (β, f (β)), C (γ, f (γ))$ $be three points on the graph of y = f (x) and$
$0 < α < β < γ . Then which of the following is true?$