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Given that the maximum value of function f (x) = the square of AX + (2a-1) x-3 in the interval [- 3 / 2,2] is 1, find the value of real number a It's urgent···
The discussion is divided into the following situations:
1. A = 0, f (x) = - x-3 is a linear function, and the maximum value on [- 3 / 2,2] is f (- 3 / 2) = - 3 / 2, which is inconsistent with the title
2. If a is not 0, then f (x) is a quadratic function and a parabola
2.1、a > 0
If f (- 3 / 2) = 1, then a = - 2, which is inconsistent with the assumption; if f (2) = 1, then a = 3 / 4, by calculating f (- 3 / 2), its value is less than 1, so a = 3 / 4 is one of the answers
2.2、a
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