1. [tex]y=5x^4-10x^3+10x^2-5x+1\Rightarrow y'=20x^3-30x^2+20x-5=5(4x^3-6x^2+4x-1)=5(2x-1)(2x^2-2x+1)[/tex]
[TEX]
\begin{array}{c|ccccc}
x & -\infty & & \frac{1}{2} & & +\infty \\
\hline
y' & & - & 0 & + & \\
\hline
y & +\infty & & & & +\infty \\
& & \searrow & & \nearrow & \\
& & & 0 & &
\end{array}
[/TEX]
2. [tex]y'=\frac{2\sqrt{x^2-x+1}+2x-1}{4\sqrt{x^2-x+1}.\sqrt{x+\sqrt{x^2-x+1}}} > 0[/tex]
[tex]\lim_{x\rightarrow -\infty}\sqrt{x+\sqrt{x^2-x+1}}=\lim_{x\rightarrow -\infty}\sqrt{\frac{1-x}{\sqrt{x^2-x+1}-x}}=\lim_{x\rightarrow -\infty}\sqrt{\frac{-\frac{1}{x}+1}{\sqrt{1-\frac{1}{x}+\frac{1}{x^2}}+1}}=\sqrt{\frac{1}{2}}[/tex]
[tex]\lim_{x\rightarrow +\infty}\sqrt{x+\sqrt{x^2-x+1}}=+\infty[/tex]
[TEX]
\begin{array}{c|ccc}
x & -\infty & & +\infty \\
\hline
y' & & + \\
\hline
& & & +\infty \\
& & \nearrow & \\
y & \frac{\sqrt{2}}{2} & &
\end{array}
[/TEX]
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
