Question

Co-ordinates of a point on the curve y=xlogx at which the normal is parallel to the line 2x-2y=3 are

Answer 1

$y=xlnx$

slope of normal=$\frac{1}{y^{\prime }}=1$

$=>y^{\prime }=-1$

$=>y^{\prime }=lnx+1$

$=>lnx+1=-1$

$=>lnx=-2$

$=>x=\frac{1}{e^2}$---------------$[lo{g}_{e}a=\frac{1}{e^a}]$

$y=\frac{-2}{e^2}$

Now equation

$(y+\frac{2}{e^2})=(x-\frac{1}{e^2})$