Question

A differentiable function $f ( x )$ is strictly increasing $\forall x \in R$, Then -

• A. $f ^{\prime}( x ) >0 \forall x \in R$
• B. $f^{\prime}(x) \geq 0 \forall x \in R$, provided it vanishes at finite number of points.
• C. $f^{\prime}(x) \geq 0 \vee x \in R$ provided it vanishes at discrete points though the number of these discrete points may not be finite.
• D. $f ^{\prime}( x ) \geq 0 \quad \forall x \in R$ provided it vanishes at discrete points and the number of these discrete points must be infinite.

Answer 1

Answer: (C)

Correct answer is (c) $f^{\prime}(x) \geq 0 \vee x \in R$ provided it vanishes at discrete points though the number of these discrete points may not be finite.