Question

Find

the minimum value of
xlogx
​

Answer 1

Answer:

sorry I can't do anything......

Answer 2

Step-by-step explanation:

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