Question

maximum value of ㏒x/x

Answer 1

Answer:

−  

e

1

​  

 

y=xlogx  

diff. both sides w.r.t. x  

dx

dy

​  

=logx+  

x

x

​  

=1+logx=loge+logx

 

dx

dy

​  

=logex⟶(1)  

Now, to find minima ⇒  

dx

dy

​  

=0

log  

e

​  

ex=0

⇒ex=1  ⇒ x=  

e

1

​  

 

diff. eqn.(1) w.r.t. x

dx  

2

 

d  

2

y

​  

=  

ex

1

​  

×e=  

x

1

​  

 ⇒ [  

dx  

2

 

d  

2

y

​  

]  

x=  

e

1

​  

 

​  

=e>0  

∴ At x=  

e

1

​  

, y is minimum  

∴ minimum  value of xlogx=  

e

1

​  

log  

e

1

​  

 

=  

e

1

​  

loge  

−1

 

=−  

e

1

​  

loge

=−  

e

1

​  

 

Step-by-step explanation: