Question

函数f(x)=x2+(3a-1)x+2a在(2,3)上为单调函数,求实数a的取值范围

Answer 1

f(x)= x^2+(3a-1)x +2a

f'(x) = 2x + 3a-1 =0

x = (1-3a)/2

f''(x) = 2 > 0 ( min)

在(2,3)上为单调函数

=>(1-3a)/2 ≤ 2 or (1-3a)/2 ≥3

=>a≥ -1 or a≤-5/3