Question

What is the condition for a function f to be decreasing if f be continuous and differentiable on (a,b)?

(a) f’(x) > 0 ∀ x1, x2 ∈ (a,b)

(b) f’(x) < 0 ∀ x1, x2 ∈ (a,b)

(c) f’(x) = 0 ∀ x1, x2 ∈ (a,b)

(d) f’(x) ≤ 0 ∀ x1, x2 ∈ (a,b)

I got this question in my homework.

The doubt is from Derivatives Application topic in portion Application of Derivatives of Mathematics – Class 12

Answer 1

Right choice is (d) f’(x) ≤ 0 ∀ x1, x2 ∈ (a,b)

To explain: If a function f be continuous and differentiable on (a,b), then f’(x) ≤ 0 ∀ x1, x2 ∈ (a,b) is the condition for the function f(x) to be decreasing on (a,b).