Question

What is the condition for a function f to be strictly decreasing 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 in an internship interview.

I want to ask this question from Derivatives Application in chapter Application of Derivatives of Mathematics – Class 12

Answer 1

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

The explanation: The mathematical expression for strictly decreasing function is f’(x) < 0 ∀ x1, x2 ∈ (a,b). This is the condition for strictly decreasing function and only possible when function ‘f’ is continuous and differentiable on (a,b).