For which value of x will (x – 1)(3 – x) have its maximum?
Question
For which value of x will (x – 1)(3 – x) have its maximum?
Solution
To find the maximum value of the function (x – 1)(3 – x), we first need to find the derivative of the function.
The function can be rewritten as -x^2 + 4x - 3.
The derivative of the function is -2x + 4.
Setting the derivative equal to zero gives us -2x + 4 = 0.
Solving for x gives us x = 2.
Therefore, the function (x – 1)(3 – x) has its maximum at x = 2.
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