v argmin and argmax - Mathematics

# argmin and argmax

`argmin` and `argmax` are the inputs, `x`'s, to a function, `f`, that creates the smallest and largest outputs, `f(x)`.

## Preliminaries

```import numpy as np
import pandas as pd
np.random.seed(1)
```

## Define A Function, f(x)

```# Define a function that,
def f(x):
# Outputs x multiplied by a random number drawn from a normal distribution
return x * np.random.normal(size=1)[0]
```

## Create Some Values Of x

```# Create some values of x
xs = [1,2,3,4,5,6]
```

## Find The Argmin Of f(x)

```#Define argmin that
def argmin(f, xs):
# Applies f on all the x's
data = [f(x) for x in xs]

# Finds index of the smallest output of f(x)
index_of_min = data.index(min(data))

# Returns the x that produced that output
return xs[index_of_min]
```
```# Run the argmin function
argmin(f, xs)
```
```6
```

## Check Our Results

```print('x','|', 'f(x)')
print('--------------')
for x in xs:
print(x,'|', f(x))
```
```x | f(x)
--------------
1 | 1.74481176422
2 | -1.52241380179
3 | 0.957117288171
4 | -0.99748150191
5 | 7.31053968522
6 | -12.360844257
```