jee-main 2020 Q63

jee-main · India · session1_09jan_shift1 Applied differentiation Convexity and inflection point analysis

Let $f$ be any function continuous on $[ a , b ]$ and twice differentiable on $( a , b )$. If all $x \in ( a , b ) , f ^ { \prime } ( x ) > 0$ and $f ^ { \prime \prime } ( x ) < 0$, then for any $c \in ( a , b ) , \frac { f ( c ) - f ( a ) } { f ( b ) - f ( c ) }$
(1) $\frac { b + a } { b - a }$
(2) 1
(3) $\frac { b - c } { c - a }$
(4) $\frac { c - a } { b - c }$

Let $f$ be any function continuous on $[ a , b ]$ and twice differentiable on $( a , b )$. If all $x \in ( a , b ) , f ^ { \prime } ( x ) > 0$ and $f ^ { \prime \prime } ( x ) < 0$, then for any $c \in ( a , b ) , \frac { f ( c ) - f ( a ) } { f ( b ) - f ( c ) }$\\
(1) $\frac { b + a } { b - a }$\\
(2) 1\\
(3) $\frac { b - c } { c - a }$\\
(4) $\frac { c - a } { b - c }$

Paper Questions

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