Applications Of Derivatives Question 138
Question: The point at which the tangent to the curve $ y=2x^{2}-x+1 $ is parallel to $ y=\text{ 3}x+\text{9 } $ will be
[Karnataka CET 2001]
Options:
A) (2, 1)
B) (1, 2)
C) (3, 9)
D) (-2, 1)
Show Answer
Answer:
Correct Answer: B
Solution:
$ y=2x^{2}-x+1 $
therefore $ \frac{dy}{dx}=4x-1 $ .
We know that this equation gives the slope of tangent to the curve. Since this tangent is parallel to $ y=3x+9, $
therefore slope of the tangent is 3, so $ 4x-1=3 $ or $ x=1. $ Therefore $ y=2x^{2}-x+1=2-1+1=2. $ Thus the point $ (x,,y) $ is (1, 2).
BETA
