Checkout JEE MAINS 2022 Question Paper Analysis : Checkout JEE MAINS 2022 Question Paper Analysis :

The total number of parallel tangents of f1(x)= x2 - x + 1 and f2(x) = x3 - x2 -2x + 1 is

(a) 2 

(b) 0

(c) 1 

(d) infinite

Solution:

Given f1(x)= x2 – x + 1 ..(i)

f2(x) = x3 – x2 -2x + 1 ..(ii)

Differentiate (i)

f1’(x) = 2x-1

f2’(x) = 3x2 – 2x – 2

f1’(x) = f2’(x)

=> 2x-1 = 3x2 – 2x – 2

Let the tangents drawn to the curves y = f1(x) and y = f2(x) at (x1, f1(x1)) and (x2, f2(x2)) be parallel. Then

2x1 -1 = 3x22 – 2x2 – 2

2x1 = 3x22 – 2x2 -1

So, there are infinite solutions.

Hence option d is the answer.

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