1. Find the maximum and minimum values, if any, of the following functions
given by
(i) f (x) = (2x - 1)^2 + 3

Answers (1)

Given function is,
f (x) = (2x - 1)^2 + 3
(2x - 1)^2 \geq 0\\ (2x-1)^2+3\geq 3
Hence, minimum value occurs when 
(2x-1)=0\\ x = \frac{1}{2}
Hence, the minimum value of function f (x) = (2x - 1)^2 + 3 occurs at  x = \frac{1}{2}
and the minimum value is 
f(\frac{1}{2}) = (2.\frac{1}{2}-1)^2+3\\
            = (1-1)^2+3 \Rightarrow 0+3 = 3
and it is clear that there is no maximum value of f (x) = (2x - 1)^2 + 3 

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