Applications Of Derivatives Question 41
Question: The total number of parallel tangents of $ f_1(x)=x^{2}-x+1 $ and $ f_2(x)=x^{3}-x^{2}-2x+1 $ is
Options:
A) 2
B) 0
C) 1
D) Infinite
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Here, $ f_1(x)=x^{2}-x+1 $ and $ f_2(x)=x^{3}-x^{2}-2x+1 $ or $ f_1’(x_1)=2x_1-1 $ and $ f_2’(x_2)=3x_2^{2}-2x_2-2 $
Let the tangents drawn to the curves $ y=f_1(x) $ and $ y=f_2(x) $ at $ (x_1,f_1(x_1)) $ and $ (x_2,f_2(x_2)) $ be parallel.
Then $ 2x_1-1=3x_2^{2}-2x_2-2 $ or $ 2x_1=(3x_2^{2}-2x_2-1) $ So, which is possible for infinite numbers of ordered pairs. So, there are infinite solutions.
BETA
