=0 2‌log‌x+(log‌x)2=0 (log‌x)[log‌x+2]=0 log‌x=0|log‌x+2=0 x=1 | log‌x=−2 & x=e−2 Using second order derivative lest. Again differentiating y w.I.t. x
d2y
dx2
=2x+2‌log‌x.
1
x
d2y
dx2
|x=1=2>0 ∴ x=1 is point of minima
d2y
dx2
|x=e−2=
2
e−2
+2.log‌e−2.
1
e−2
=
1
e−2
(2−4)=−
2
e−2
<0 ∴ x=e−2 is point of maxima. ∴ ymax=e−2(log‌e−2)2 =e−2(−2)2=4e−2