Question

What is the mathematical expression for monotonically decreasing 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 semester exam.

This interesting question is from Derivatives Application in division Application of Derivatives of Mathematics – Class 12

Answer 1

The correct option is (b) x1 < x2 ⇒ f(x1) ≥ f(x2) ∀ x1, x2 ∈ (a,b)

Easy explanation: The definition of monotonically decreasing function is if a function f : (a,b) → R is said to be monotonically decreasing on (a,b) if x1 < x2 ⇒ f(x1) ≥ f(x2) ∀ x1, x2 ∈ (a,b). Hence, the mathematical expression is x1< x2 ⇒ f(x1) ≥ f(x2) ∀ x1, x2 ∈ (a,b).