A function \(f\) defined on a subset E of real numbers has a minimum m at a point \(a\) in E if m = \(f(a)\) and if, for all \(x\) in E, \(f(x)\) is greater than or equal to \(f(a)\).
Therefore, m is the minimum of the set of images of f.
Example
Consider the function defined by \(f(x)\) = \(x^{2}\)+ 4, and represented by the parabola below:
If \(x\) = 0, then \(f(x)\) = 4
For any other value of \(x\), \(f(x)\) > 4.
Therefore, the minimum of the image of this function is 4.
We can also say that 4 is the minimum of the function f.
The function defined by \(f(x)\) = –\(x^{2}\)+ 4, does not have a minimum, but its
