Applications Of Derivatives Question 153
Question: If a tangent to the curve $ y=6x-x^{2} $ is parallel to the line $ 4x-2y-1=0 $ , then the point of tangency on the curve is
[Karnataka CET 2004]
Options:
A) (2, 8)
B) (8, 2)
C) (6, 1)
D) (4, 2)
Show Answer
Answer:
Correct Answer: A
Solution:
Given $ y=6x-x^{2} $ …..(i) $ \frac{dy}{dx}=6-2x $ Since, tangent is parallel to the line x $ 4x-2y-1=0 $ \ $ \frac{dy}{dx}=6-2x=\frac{-4}{-2}\Rightarrow 6-2x=2\Rightarrow x=2 $
Put the value of x in (i), we get $ y=8 $
Hence required point of tangency will be $ (2,,8) $ .
BETA
