Question

fx=x2-2kx+k-1,当x属于[-1.2]时,有最小值-4,求k

Answer 1

f(x)=x^2-2kx+k^2-k^2+k-1=(x-k)^2-k^2+k-1=0

x属于[-1,2]时,有最小值

-1≤k≤2

此时,有最小值-k^2+k-1=-4

整理,得

k^2-k-3=0

(k-1/2)^2=13/4

k=(1+√13)/2>2(舍去)或k=(1-√13)/2

k=(1-√13)/2