tìm min A=2x^2 + 3x + 15 tìm max D= 4+2x-x^2 tìm max E= 1+3x-2x^2

Question

tìm min A=2x^2 + 3x + 15
tìm max D= 4+2x-x^2
tìm max E= 1+3x-2x^2

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Delilah 3 tuần 2021-11-21T07:14:23+00:00 2 Answers 3 views 0

Answers ( )

    0
    2021-11-21T07:15:27+00:00

    Đáp án:

    `A=2x^2 + 3x + 15`

    `⇒2(x²+3/2x)+15`

    `⇒2(x+3/4)²+111/8≥111/8`

    Dấu `”=”` xảy ra khi :

    `x+3/4=0`

    `⇒x=-3/4`

    `⇒A_{min}=111/8` khi `x= -3/4`

    `D= 4+2x-x^2`

    `⇒-(x²-2x-4)`

    `⇒-(x²-2x-1)-3`

    `⇒-(x-1)²-3≤-3`

    DẤu `”=”` xảy ra khi :

    `x-1=0`

    `⇒x=1`

    Vậy` D_{max}=-3` khi `x=1`

    `E= 1+3x-2x^2`

    `⇒-2(x²-3/2x)+1`

    `⇒-2(x-3/4)²+17/8≤17/8`

    Dấu `”=”` xảy ra khi :

    `x-3/4=0`

    `⇒x=3/4`

    Vậy `E_{max}=17/8` khi `x= 3/4`

     

    0
    2021-11-21T07:15:28+00:00

    ` A = 2x^2 + 3x + 15`

    ` = 2(x^2 + 3/(2)x) + 15`

    ` = 2(x^2 + 2.3/(4)x + 9/16) – 9/8 + 15`

    ` = 2.(x+3/4)^2 + 111/8 \geq 111/8`

    ` => A_{min} = 111/8` ; khi ` x = -3/4`

    ` D  = 4 + 2x – x^2 = -(x^2 – 2x -4) = -(x^2-2x +1) -3`

    ` = -(x-1)^2 -3 \leq -3`

    ` => D_{max}= -3` khi ` x = 1`

    ` E =  1 + 3x – 2x^2 = -2(x^2 – 3/(2)x ) + 1`

    ` = -2.(x^2 -3/(2)x + 9/16) + 9/8 + 1`

    ` = -2(x-3/4)^2 + 17/8 \leq 17/8`

    `=> E_{max} = 17/8` khi ` x  = 3/4`

     

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