Question

What is the mathematical expression for a function to be strictly decreasing on (a,b)?

(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)

This question was addressed to me during an interview.

My question is based upon Derivatives Application topic in chapter Application of Derivatives of Mathematics – Class 12

Answer 1

The correct answer is (b) x1 < x2 ⇒ f(x1) > f(x2) ∀ x1, x2 ∈ (a,b)

To explain: There are two types of decreasing functions in maxima and minima. They are strictly decreasing and monotonically decreasing. The mathematical expression for strictly decreasing function is x1 < x2 ⇒ f(x1) > f(x2) ∀ x1, x2 ∈ (a,b).