isi-entrance 2016 Q49

isi-entrance · India · UGB 4 marks Applied differentiation MCQ on derivative and graph interpretation
Let $f : ( 0, 2 ) \cup ( 4, 6 ) \rightarrow \mathbb { R }$ be a differentiable function. Suppose also that $f ^ { \prime \prime } ( x ) = 1$ for all $x \in ( 0, 2 ) \cup ( 4, 6 )$. Which of the following is ALWAYS true?
(A) $f$ is increasing
(B) $f$ is one-to-one
(C) $f ( x ) = x$ for all $x \in ( 0, 2 ) \cup ( 4, 6 )$
(D) $f ( 5.5 ) - f ( 4.5 ) = f ( 1.5 ) - f ( 0.5 )$
Let $f : ( 0, 2 ) \cup ( 4, 6 ) \rightarrow \mathbb { R }$ be a differentiable function. Suppose also that $f ^ { \prime \prime } ( x ) = 1$ for all $x \in ( 0, 2 ) \cup ( 4, 6 )$. Which of the following is ALWAYS true?\\
(A) $f$ is increasing\\
(B) $f$ is one-to-one\\
(C) $f ( x ) = x$ for all $x \in ( 0, 2 ) \cup ( 4, 6 )$\\
(D) $f ( 5.5 ) - f ( 4.5 ) = f ( 1.5 ) - f ( 0.5 )$