Question

What is the mathematical expression of  non-decreasing function?

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

(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 during an online exam.

The question is from Derivatives Application topic in section Application of Derivatives of Mathematics – Class 12

Answer 1

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

The explanation is: A function f : (a,b) → R is said to be monotonically increasing on (a,b) if x1 < x2 ⇒ f(x1) ≤ f(x2) ∀ x1, x2 ∈ (a,b). A monotonically increasing function can also be called as non-decreasing function.