Question

tìm GTNN(hoặc GTLN)cúa

a)A=x²-x+1

b)B=x²+2|x|+2

c)C=(x-1)(x-2)(x-3)(x-4)+15

d)D=1-x²-x⁴

Answer 1

\(A=x^2-x+\frac{1}{4}+\frac{3}{4}=\left(x-\frac{1}{2}\right)^2+\frac{3}{4}\ge\frac{3}{4}\)

\(B=x^2+2\left|x\right|+2\)

Do \(\left\{{}\begin{matrix}x^2\ge0\\\left|x\right|\ge0\end{matrix}\right.\) \(\Rightarrow B\ge2\)

\(C=\left(x-1\right)\left(x-4\right)\left(x-2\right)\left(x-3\right)+15\)

\(=\left(x^2-5x+4\right)\left(x^2-5x+6\right)+15\)

\(=\left(x^2-5x+4\right)^2+2\left(x^2-5x+4\right)+1+14\)

\(=\left(x^2-5x+5\right)^2+14\ge14\)

\(D=1-\left(x^2+x^4\right)\)

Do \(\left\{{}\begin{matrix}x^4\ge0\\x^2\ge0\end{matrix}\right.\) \(\Rightarrow x^2+x^4\ge0\Rightarrow D\le1\)