y = f(x) is a parabola, having it's axis parallel to y-axis…

Maths Differentiation and Applications of Derivatives General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 14, 2026

y = f(x) is a parabola, having it's axis parallel to y-axis. If the line y = x touches this parabola at x = 1, then

f”(1) – f’ (0) = 1

f”(0) – f’(1) = 1

f”(1) + f’(0) = 1

f”(0) + f’(1) = 1

Text Solution

Verified by Experts

The correct answer is:

Let y = f(x) = ax 2 + bx + c. We have f(1) = 1

⇒ ⇒ a + b + c = 1. Also ax 2 + bx + c = x should have x – 1 as it's repeated root.

⇒ ⇒ ax 2 + (b – 1)x + c = a(x – 1) 2

⇒ ⇒ 1 – b = 2a, a = c.

We have f '(x) = 2ax + b, f'(x) = 2a

⇒ ⇒ f(1) = 2a, f(0) = b

⇒ ⇒ f "(1) + f(O) = 1.

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