Question
Question: Total number of parallel tangents of f<sub>1</sub>(x) = x<sup>2</sup>− x + 1 and f<sub>2</sub>(x) = ...
Total number of parallel tangents of f1(x) = x2− x + 1 and f2(x) = x3− x2− 2x + 1 is equal to
A
2
B
3
C
4
D
None of these
Answer
None of these
Explanation
Solution
f1'(x1) = 2x1 − 1, f2'(x2) = 3x22 − 2x2 − 2.
Let tangents drawn to the curves y = f1(x) and y = f2(x) at (x1, f(x1)) and (x2, f(x2)) are parallel, then 2x1 -1 = 3x22 − 2x2 − 2, which is possible for infinite number of ordered pair (x1, x2).