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第四章:部分分式 Partial Fraction

第六章:角的形成及单位 Angles and Measurements

第十三章: 方程组 Simultaneous Equations

第十五章:二元一次不等式及线性规划 linear inequality in two variables and linear programming

14.9 代数式的最大值和最小值 Rational Quadratic Functions

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) = \frac{4x^2-2x+1}{4x^2+2x+1}, where x\epsilonR.

求函数f (x) = \frac{4x^2-2x+1}{4x^2+2x+1} , 其中 x\epsilonR的最大值和最小值.

Answer:
3, \frac{1}{3}
(2) Find the possible range of values of \frac{\left(x+1\right)^2}{x^2+x+1} if x is real.

若x 是实数求 \frac{\left(x+1\right)^2}{x^2+x+1} 的可能范围。

Answer:
0, 1\frac{1}{3}
(3) Find the range of \lambda where \frac{x+\lambda}{x^2-\lambda} is real for x\epsilonR.

\frac{x+\lambda}{x^2-\lambda}为实数当 x\epsilonR,求 \lambda 的范围

Answer:
0 < \lambda \leq 1
(4) Find the range of \lambda where \frac{x+\lambda}{x^2+x-\lambda} is real for x\epsilonR.

\frac{x+\lambda}{x^2+x-\lambda} 为实数当 x\epsilonR,求\lambda的范围.

Answer:
0 \leq \lambda \leq 2