Question

What is the condition for a function f to be increasing if f be continuous and differentiable on (a,b)?

(a) f’(x) < 0 ∀ x1, x2 ∈ (a,b)

(b) f’(x) > 0 ∀ x1, x2 ∈ (a,b)

(c) f’(x) = 0 ∀ x1, x2 ∈ (a,b)

(d) f’(x) ≥ 0 ∀ x1, x2 ∈ (a,b)

The question was posed to me during an online exam.

The query is from Derivatives Application in chapter Application of Derivatives of Mathematics – Class 12

Answer 1

The correct answer is (d) f’(x) ≥ 0 ∀ x1, x2 ∈ (a,b)

For explanation: If a function f be continuous and differentiable on (a,b), then f’(x) ≥ 0 ∀ x1, x2 ∈ (a,b) is the condition for the function f(x) to be increasing on (a,b).