(1) If the monotone decreasing interval of the function f(x) is (-∞, 2), find the maximum value of the function f(x) in the interval.

The function is a single increasing function at [2, +∞].

So the maximum value is f (5) = 25-10a+3 = 28-10a.

(2) If the function f(x) is a decreasing function (-∞, 2) in the interval, find the maximum value of f (1).

Explain that its symmetry axis is greater than or equal to 2, so

f(x)=x？ -2ax+3 =x^2-2ax+a^2-a^2+3=(x-a)^2-a^2+3

So a≥2

f( 1)= 1-2a+3=4-2a≤0

So the maximum value is 0.