Question

What is the mathematical expression for monotonically non-increasing function?

(a) x1 < x2 ⇒ f(x1) ≤ f(x2) ∀ x1, x2 ∈ (a,b)

(b) x1 < x2 ⇒ f(x1) ≥ f(x2) ∀ x1, x2 ∈ (a,b)

(c) x1 = x2 ⇒ f(x1) ≤ f(x2) ∀ x1, x2 ∈ (a,b)

(d) x1 < x2 ⇒ f(x1) = f(x2) ∀ x1, x2 ∈ (a,b)

I got this question in examination.

This intriguing question comes from Derivatives Application topic in division Application of Derivatives of Mathematics – Class 12

Answer 1

Correct answer is (b) x1 < x2 ⇒ f(x1) ≥ f(x2) ∀ x1, x2 ∈ (a,b)

For explanation I would say: The meaning of a monotonic function is it either never decreases or never increases. The condition for a function to be monotonically non-increasing is x1 < x2 ⇒ f(x1) ≥ f(x2) ∀ x1, x2 ∈ (a,b).