A good God in solving a mathematical problem helps to find the maximum and minimum value of the known function f (x) = x2-2x + 3 on [a, a + 3] I have the answer. I will discuss it in four intervals, but I don't know where the boundary of minus half comes from The four intervals are (negative infinity, - 2) [- 2, negative half] (negative half, 1)] (1, positive infinity) How did that negative half come from? (X2 is the square of x) | Math enthusiast | Mathematical art

A good God in solving a mathematical problem helps to find the maximum and minimum value of the known function f (x) = x2-2x + 3 on [a, a + 3] I have the answer. I will discuss it in four intervals, but I don't know where the boundary of minus half comes from The four intervals are (negative infinity, - 2) [- 2, negative half] (negative half, 1)] (1, positive infinity) How did that negative half come from? (X2 is the square of x)

Well, it's troublesome. I'll only explain to you one half of it
According to - 2A / b = 1, the axis of symmetry of the function is 1
At this time, it will be divided into three cases, namely a + 31
However, when a ≤ 1 ≤ a + 3, it can be divided into two cases: a + A + 3 / 2 = a + 3 / 2 ≤ 1 and ≥ 1
The reason why you want to consider this is that you can draw a graph. When a + 3 / 2 ≤ 1, the maximum value will be x = a,
When a + 3 / 2 ≥ 1, the maximum value is x = a + 3, so there will be a negative half

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