Applications Of Derivatives Question 122
Question: Co-ordinates of a point on the curve $ y=x\log x $ at which the normal is parallel to the line $ 2x-2y=3 $ are
[RPET 2000]
Options:
A) (0,0)
B) $ (e,e) $
C) $ (e^{2},,2e^{2}) $
D) $ ({e^{-2}}-2{e^{-2}}) $
Show Answer
Answer:
Correct Answer: D
Solution:
$ y=x\log x $
therefore $ \frac{dy}{dx}=1+\log x $
The slope of the normal = $ -\frac{1}{(dy/dx)}=\frac{-1}{1+\log x} $
The slope of the line $ 2x-2y=3 $ is 1. \ $ \frac{-1}{1+\log x}=1 $
therefore $ \log x=-2 $
therefore $ x={e^{-2}} $ \ $ y=-2{e^{-2}} $ \ Co-ordinate of the point is $ ({e^{-2}},,-2{e^{-2}}) $ .
BETA
