Question

若函数f(x)=ax^5-bx^3+c(a不等于0)在x=正负1时有极值,极大值为4,极小值为6,试求函数f(x)的解析

Answer 1

f(x)‘=5ax∧4-3b∧2 则x=±1,f(x)'=0,5a-3b=0,x=1时,f(x)=4,x=-1时,f(x)=6,

则a=1.5 b=2.5 c=5则f（x）=1.5x∧5-2.5x∧3+5；同理x=1时f(x)=6,x=-1时f(x)=4,a=-1.5,

b=-2.5则f（x）=-1.5x∧5+2.5x∧3+5