Question

f(x)等于负x的平方加二ax和g(x)等于(二a减一)乘以x加一在区间[1,2]上都是减函数,求a的范围

Answer 1

我来告诉你:

f(x)=-x^2+2ax,

根据b^2-4ac≥0则有,a≥0.

f(x)的对称轴是x=a.

要使f(x)在区间[1,2]上为减函数,则需满足a≤1,

而,g(x)=(2a-1)x+1,在区间[1,2]上是减函数,

则需满足2a-1