Test Index

AP and TS EAMCET Engineering Model Paper 8

© examsnet.com

Question : 57 of 160

Marks: +1, -0

The total number of parallel tangents of

f_1(x)=x^2-x+1

f_2(x)=x^3-x^2-2x+1

are

2
0
1
infinite

Solution:

f_1(x)=x^2-x+1,

f_2(x)=x^3-x^2-2x+1

\Rightarrow f_{11}(x)=2x-1, f_{21}(x)=3x^2-2x-2

Let the tangents drawn to the curve

y=f_1(x) \; ; \; y=f_2(x)

\text{At} (x_1,y_1) \; ; \; (x_2,y_2)

are parallel

\Rightarrow 2x_1-1=3x_2^2-2x_2-2

\Rightarrow 2x_1=3x_2^2-2x_2-1

Which is possible for infinite numbers of ordered pairs

⇒ Infinite solutions

© examsnet.com

Go to Question:

Prev Question

Next Question