A differentiable function f ( x ) is strictly increasing ∀ x ∈ R, Then -

Question

A differentiable function f ( x ) is strictly increasing ∀ x ∈ R, Then - (A) f prime( x ) >0 ∀ x ∈ R (B) f prime(x) ≥ 0 ∀ x ∈ R, provided it vanishes at finite number of points. (C) f prime(x) ≥ 0 ∨ x ∈ R provided it vanishes at discrete points though the number of these discrete points may not be finite. (D) f prime( x ) ≥ 0 ∀ x ∈ R provided it vanishes at discrete points and the number of these discrete points must be infinite.

Tardigrade Admin · Accepted Answer

Correct answer is (c) f prime(x) ≥ 0 ∨ x ∈ R provided it vanishes at discrete points though the number of these discrete points may not be finite.

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

$f^{'} (x) > 0\forall x \in R$

$f^{'} (x) \geq 0\forall x \in R$ , provided it vanishes at finite number of points.

$f^{'} (x) \geq 0 \lor x \in R$ provided it vanishes at discrete points though the number of these discrete points may not be finite.

$f^{'} (x) \geq 0 \forall x \in R$ provided it vanishes at discrete points and the number of these discrete points must be infinite.

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

Q. A differentiable function f(x) is strictly increasing ∀x∈R, Then -

f′(x)>0∀x∈R

f′(x)≥0∀x∈R, provided it vanishes at finite number of points.

f′(x)≥0∨x∈R provided it vanishes at discrete points though the number of these discrete points may not be finite.

f′(x)≥0∀x∈R provided it vanishes at discrete points and the number of these discrete points must be infinite.