# What is the minimum of this function?

## What is the minimum of this function?

A global minimum of a function is the smallest value in the entire range of the function, while a local minimum is the smallest value in some local neighborhood.

**How do you find the minimum of a function?**

The minimum value of a function is found when its derivative is null and changes of sign, from negative to positive. Example: f(x)=x2 f ( x ) = x 2 defined over R , its derivative is f′(x)=2x f ′ ( x ) = 2 x , that is equal to zero in x=0 because f′(x)=0⟺2x=0⟺x=0 f ′ ( x ) = 0 ⟺ 2 x = 0 ⟺ x = 0 .

**What is maximum and minimum of a function?**

A maximum is a high point and a minimum is a low point: In a smoothly changing function a maximum or minimum is always where the function flattens out (except for a saddle point).

### Can there be two absolute minimums?

Again, the function doesn’t have any relative maximums. As this example has shown there can only be a single absolute maximum or absolute minimum value, but they can occur at more than one place in the domain.

**What is the maximum value of a function?**

The maximum value of a function is the place where a function reaches its highest point, or vertex, on a graph. If your quadratic equation has a negative a term, it will also have a maximum value. There are three ways to find that maximum, depending on which form of a quadratic you have.