Question

函数y=a的x-1次方(a>0且a不等于1)的图像恒过定点A.(1)写出定点A的坐标;(2)若点A在直线mx+ny-1=

Answer 1

(1) x = 1,y = 1 (与a的值无关,A(1,1)

(2) 带入直线方程:m + n- 1 = 0

n = 1 - m

1/m + 1/n = (m + n)/(mn) = 1/(mn)

1/m+1/n取最小值时,mn取最大值

mn = m(1 - m) = -(m - 1/2)² + 1/4

mn最大值为1/4,1/m+1/n最小值为 1/(1/4) = 4