tìm min A=2x^2 + 3x + 15 tìm max D= 4+2x-x^2 tìm max E= 1+3x-2x^2 21/11/2021 Bởi Delilah tìm min A=2x^2 + 3x + 15 tìm max D= 4+2x-x^2 tìm max E= 1+3x-2x^2
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` Bình luận
` 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` Bình luận
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`
` 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`