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

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

Answers (1)
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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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