Question

What is the condition for a function f to be constant 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 had been asked this question in examination.

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

Answer 1

Correct choice is (c) f’(x) = 0 ∀ x1, x2 ∈ (a,b)

For explanation I would say: One of the properties of a function is to be constant. A function is said to be constant when it satisfies the condition f’(x) = 0 ∀ x1, x2 ∈ (a,b) where the function ‘f’ should be continuous and differentiable on (a,b).