Let y = f(x) & y = g(x) be two curves such that f(x) = x 2 …

Maths Differentiation and Applications of Derivatives General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

Let y = f(x) & y = g(x) be two curves such that f(x) = x 2 – x + 1 and g(x) = x 3 – x 2 – 2x + 1, then

Tangent lines to y = f(x) at any two distinct points can't coincide

Tangent lines to y = g(x) at any two distinct points can't coincide

y = f(x) and y = g(x) may have infinite number of parallel tangents

There may be few lines which may touch these curves twice

Text Solution

Verified by Experts

The correct answer is:

CHECK THE SOLUTION.

(a,b,c)

It is a parabola hence every tangent to it has a unique contact point.

Let y = mx + c be a tangent to y = g(x) touching it at two distinct points, then

mx + c = x 3 – x 2 – 2x + 1 must have two pairs of repeated roots which is not possible

Let tangent to y = f(x) at P(x 1 , y 1 ) and
y = g(x) at Q(x 2 , y 2 ) are parallel then

2x 1 – 1 = 3x 2 2 – 2x 2 – 2

can have infinitely many solutions for x 1 & x 2

Using & it can be concluded as a wrong statement

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