Let f(x) = (1 + b 2 )x 2 + 2bx + 1 and let m(b) be the mini…

Maths Differentiation and Applications of Derivatives Maxima and Minima Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

Let f(x) = (1 + b 2 )x 2 + 2bx + 1 and let m(b) be the minimum value of f(x). As b varies, the range of m(b) is

[0, 1]

(0, 1]

Text Solution

Verified by Experts

The correct answer is:

Since coefficient of x 2 is (+ve)

⇒ m(b) = m(b) = – ⇒ m(b) =

⇒ ⇒ 1 + b 2 ≥ 1 ⇒ ⇒ m(b) ∈ (0, 1]

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