About Lesson
14.9 Rational Quadratic Functions 代数式的最大值和最小值
(1)
Find the maximum and minimum values of function f (x) = , where x
R.
求函数f (x) = , 其中 x
R的最大值和最小值.
Answer:
3, ![Rendered by QuickLaTeX.com \frac{1}{3}](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI5IiBoZWlnaHQ9IjI5IiB2aWV3Qm94PSIwIDAgOSAyOSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2VhZWFlYyIvPjwvc3ZnPg==)
![Rendered by QuickLaTeX.com \frac{1}{3}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-e63e48332471cc9171675f2cb9c542fd_l3.png)
(2) Find the possible range of values of
if x is real.
![Rendered by QuickLaTeX.com \frac{\left(x+1\right)^2}{x^2+x+1}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-c4d6778f69275af95072fbb7baadae8b_l3.png)
若x 是实数求 的可能范围。
Answer:
0, 1![Rendered by QuickLaTeX.com \frac{1}{3}](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI5IiBoZWlnaHQ9IjI5IiB2aWV3Qm94PSIwIDAgOSAyOSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2VhZWFlYyIvPjwvc3ZnPg==)
![Rendered by QuickLaTeX.com \frac{1}{3}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-e63e48332471cc9171675f2cb9c542fd_l3.png)
(3) Find the range of
where
is real for x
R.
![Rendered by QuickLaTeX.com \lambda](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-1d098d68ee0ed12e2e3c64a6f623cf83_l3.png)
![Rendered by QuickLaTeX.com \frac{x+\lambda}{x^2-\lambda}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-64017edd4d84ffaf5a46f4f027220dab_l3.png)
![Rendered by QuickLaTeX.com \epsilon](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-0bd890136d8c87f18b3538e47d49f83b_l3.png)
若为实数当 x
R,求
的范围
Answer:
![Rendered by QuickLaTeX.com 0 < \lambda \leq 1](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-63d41cb0ab35a2597806bdc2186223b1_l3.png)
(4) Find the range of
where
is real for x
R.
![Rendered by QuickLaTeX.com \lambda](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-1d098d68ee0ed12e2e3c64a6f623cf83_l3.png)
![Rendered by QuickLaTeX.com \frac{x+\lambda}{x^2+x-\lambda}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-162a7c1ecd80c5f9598f52138c2db779_l3.png)
![Rendered by QuickLaTeX.com \epsilon](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-0bd890136d8c87f18b3538e47d49f83b_l3.png)
若 为实数当 x
R,求
的范围.
Answer:
![Rendered by QuickLaTeX.com 0 \leq \lambda \leq 2](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-778109d9722707d89d5ade8b07d95865_l3.png)