Question

What is the relation between f(x) and ℓ when the minimum value or least value function f is defined on a set A and ℓ ∈ f(A)?

(a) f(x) < &ell; ∀ x ∈ A

(b) f(x) ≤ &ell; ∀ x ∈ A

(c) f(x) ≥ &ell; ∀ x ∈ A

(d) f(x) > &ell; ∀ x ∈ A

This question was addressed to me in an interview.

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

Answer 1

Right option is (c) f(x) ≥ &ell; ∀ x ∈ A

The best I can explain: The relation between f(x) and &ell; when the minimum value or least value function f is f(x) ≥ (&ell;) ∀ x ∈ A where the function is defined on a set A and &ell; ∈ f(A).