QJEEM20Ma6d0c: JEE Main 2020 Mathematics - Class 12 JEEM20Ma6d0c Solution: Let ƒ be any function continuous on [a, b] and twice…

Question

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Let ƒ be any function continuous on [a, b] and twice differentiable on (a, b). If for all x

\in

(a, b), ƒ'(x) > 0 and ƒ''(x) < 0, then for any c

\in

(a, b),

{{f(c) - f(a)} \over {f(b) - f(c)}}

is greater than :

Accepted Answer

It is clear from graph that, slope of AC

&gt;

slope of CB

\Rightarrow

{{f\left( c \right) - f\left( a \right)} \over {c - a}}

&gt;

{{f\left( b \right) - f\left( c \right)} \over {b - c}}

\Rightarrow

{{f\left( c \right) - f\left( a \right)} \over {f\left( b \right) - f\left( c \right)}}

&gt; {{c - a} \over {b - c}}

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