Given that f (x) = CX-1 / x + 1 (C is a constant), if the maximum value of function f (x) on [0,2] is 3, find the value of C Please point in detail, satisfaction can add points, Baidu has the answer to read, please do not paste, thank you!

First of all, simplify f (x) = (CX-1) / (x + 1) = C + (- C-1) / (x + 1), and because the maximum value of F (x) on [0,2] is 3, when C belongs to (negative infinity, - 1), (- C-1) is positive, so when x = 0, f (x) has the maximum value, which is inconsistent with the proposal, so C belongs to (- 1, positive infinity) and (- C-1) is negative, so when x = 2, f (x) has the maximum value, which is substituted into C = 5

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