Find the minimum value of xlogx ​

Question

Find

the minimum value of
xlogx

in progress 0
Vivian 2 months 2021-09-10T18:35:36+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-09-10T18:37:16+00:00

    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

    0
    2021-09-10T18:37:29+00:00

    Answer:

    sorry I can’t do anything……

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