Mighty Min
Consider the function defined as
As ranges over all real values, what is the minimum value of ?
The answer is 8.
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1 solution
We know that squares are always non-negative. This implies that f ( x ) ≥ 4 directly. However, this does not imply that the minimum value must be 4.
In fact, we know that x 2 + 2 x + 3 = ( x + 1 ) 2 + 2 . Hence, ( x 2 + 2 x + 3 ) 2 achieves a minimum value of 2 2 when x = − 1 . As such, f ( x ) ≥ 2 2 + 4 = 8 , with equality when x = − 1 .