Find the maximum and minimum values, if any, of the function give… - Vidyadip

Question

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

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Answer

Given: $f(x) = (2x - 1)^2 + 3$
$\text{since}\ \ (2\text{x}-1)^2\geq\ 0\text{ for all }\text{x}\in \text{R}$
Adding 3 both sides, $(2\text{x} - 1)^2 + 3 \geq 0+3\ \Rightarrow \ \text{f}(\text{x}) \geq3$
Therefore, the minimum value of $\text{f}(\text{x}) \text{ is 3 when }2\text{x} -1 = 0, \text{i.e.,} \text{ x} =\frac{1}{2}$
This function does not have a maximum value.

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