Question

For the function f(x) = x^2 – 2x + 1. We have Rolles point at x = 1. The coordinate axes are then rotated by 45 degrees in anticlockwise sense. What is the position of new Rolles point with respect to the transformed coordinate axes?

(a) ^3⁄2

(b) ^1⁄2

(c) ^5⁄2

(d) 1

I had been asked this question in my homework.

Enquiry is from Lagrange’s Mean Value Theorem in chapter Differential Calculus of Engineering Mathematics

Answer 1

The correct option is (a) ^3⁄2

Easiest explanation: The coordinate axes are rotated by 45 degree then the problem transforms into that of Lagrange mean value theorem where the point in some interval has the slope of tan(45).

Hence differentiating the function and equating to tan(45).

We have

f'(x) = tan(45) = 2x – 2

2x – 2 = 1

x = ^3⁄2.