论文部分内容阅读
“数”和“形”在一定的条件下可以相互转化,相互渗透的。对于一些求函数的最值问题,如果把它化为几何问题,这样既避免繁杂冗长的推导与计算,解法更简捷,而且形象,直观,容易理解和掌握。从而达到化难为易的目的。例1 求函数y=(x~2+4)~(1/(x~2+4))+(x~2-8x+7)~(1/(x~2-8x+7))的最小值。分析:由y=((x-0)~2+(0-2)~2)~(1/((x-0)~2+(0-2)~2)+((x-4)~2+(0+1)~2)~(1/((x-4)~2+(0+1)~2))问题转化为:y的值是平面直角坐标系中的x轴上一点到两定点A(0,2),B(4,-1)的距离和。
“Number” and “shape” can be mutually transformed and infiltrated under certain conditions. For some problem of finding the maximum value of a function, if it is transformed into a geometric problem, this will not only avoid complicated and lengthy derivation and calculation, but also make the solution simpler and more intuitive, more intuitive and easier to understand and grasp. In order to achieve the purpose of making things difficult. Example 1 Find the function y=(x~2+4)~(1/(x~2+4))+(x~2-8x+7)~(1/(x~2-8x+7)) The minimum value. Analysis: From y=((x-0)~2+(0-2)~2)~(1/((x-0)~2+(0-2)~2)+((x-4) The problem of ~2+(0+1)~2)~(1/((x-4)~2+(0+1)~2)) translates into: the value of y is on the x-axis in a plane rectangular coordinate system. The distance from one point to two fixed points A(0,2) and B(4,-1).