Toán Lớp 8: tìm gtln
a) 6x – x^2 – 5
b) 4x – x^2 + 3
c) x – x^2
d)11 – 10x – x^2
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Toán Lớp 8: tìm gtln
a) 6x – x^2 – 5
b) 4x – x^2 + 3
c) x – x^2
d)11 – 10x – x^2
Comments ( 2 )
⇒ – (x-3)^2 \le 0 ∀ x
⇒ -(x-3)^2 + 4 \le 4 ∀ x
-> A_{max} = 4 . \text{ Dấu “=” xảy ra khi:}
(x-3)^2 = 0
b, Đặt: B= 4x – x^2 + 3
Ta có:
⇒-(x-2)^2 \le 0 ∀ x
⇒ -(x-2)^2 + 7 \le 7 ∀ x
⇒ B_{max} = 7 .\text{ Dấu “=” xảy ra khi:}
(x-2)^2 = 0
c, Đặt: C = x – x^2
C = -(x^2 – x )
⇒ – (x-1/2)^2 \le 0 ∀ x
⇒ -(x-1/2)^2 + 1/4 \le 1/4 ∀ x
⇒ C_{max} = 1/4 . \text{ Dấu “=” xảy ra khi}
(x-1/2)^2 = 0
d, Đặt: D= 11 – 10x – x^2
⇒ – (x+5)^2 \le 0 ∀ x
⇒ -(x+5)^2 + 36 \le 36 ∀ x
⇒ D_{max} = 36 . \text{ Dấu “=” xảy ra khi:}