Question

设函数f(x)=x(x-a)的平方在x=2处有极大值,求实数a的值.

Answer 1

f(x) = x(x - a) = x^2 - ax = (x - a/2)^2 - a^2/4 当x = a/2 时,f(x)有极小值.所以x = a/2 = 2 ==> a =4.min[f(x)] = -a^2/4 = -4^2 / 4 = - 4