求解一道AP微积分题!Determine A and B so that th curve y=A*x^(1/5)+B*x^(-1_数学解答

求解一道AP微积分题!
Determine A and B so that th curve y=A*x^(1/5)+B*x^(-1/5) has a point of inflection at (1,8).

人气：441 ℃　时间：2020-06-02 00:04:33

解答

首先当x=1时函数值是8,带入x=1 y=8得：A+B=8 ①
接着(1,8)是这个函数的拐点,也就是说y''(1)=0
y对x求二阶导,把x=1带入 y''=-4A/25+6B/25=0 ,即-2A+3B=0 ②
联立①②两式得：A=24/5,B=16/5