Question

Find the maximum value of

a) A=\(4x-x^2+3\)

b) B= \(x-x^2\)

c) C= \(2x-2x^2-5\)

d) D = \(4x-x^2-5\)

e) E = \(-x^2-6x-10\)

f) F = \(8x-x^2-20\)

g) G = \(4x-2x^2+3\)

h) H = \(12x-12^2+2\)

i) I = \(-x^2+7x+12\)

k) K= \(-3x^2-9x-25\)

Answer 1

a: \(A=-\left(x^2-4x-3\right)\)

\(=-\left(x^2-4x+4-7\right)\)

\(=-\left(x-2\right)^2+7< =7\)

Dấu '=' xảy ra khi x=2

b: \(B=-\left(x^2-x+\dfrac{1}{4}-\dfrac{1}{4}\right)=-\left(x-\dfrac{1}{2}\right)^2+\dfrac{1}{4}< =\dfrac{1}{4}\)

Dấu '=' xảy ra khi x=1/2

c: \(C=-2\left(x^2-x+\dfrac{5}{2}\right)\)

\(=-2\left(x^2-x+\dfrac{1}{4}+\dfrac{9}{4}\right)\)

\(=-2\left(x-\dfrac{1}{2}\right)^2-\dfrac{9}{2}< =-\dfrac{9}{2}\)

Dấu '=' xảy ra khi x=1/2

e: \(E=-\left(x^2+6x+9+1\right)=-\left(x+3\right)^2-1< =-1\)

Dấu = xảy ra khi x=-3