Question

What is the condition for a function f to be strictly 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 asked during an interview for a job.

The origin of the question is Derivatives Application in portion Application of Derivatives of Mathematics – Class 12

Answer 1

Right answer is (a) f’(x) > 0 ∀ x1, x2 ∈ (a,b)

The explanation: The condition for a function ‘f’ to be strictly increasing is f’(x) > 0 ∀ x1, x2 ∈ (a,b) where the the function ‘f’ should be continuous and differentiable on (a,b).