# How do you determine the minimum value of the function f(x)= 4^x -8?

##### 1 Answer

Mar 30, 2018

Compute the first derivative

Set that equal to zero and the value(s) of x.

Use the second derivative test to determine whether it is a minimum.

#### Explanation:

Given

Differentiate:

The derivative of a constant is 0:

Let

Use logarithmic differentiation:

Set equal to 0:

Therefore, there is no minimum or maximum.

Please look at the graph:

graph{4^x-8 [-22.8, 22.81, -11.4, 11.42]}

Please observe that it has two asymptotes but no local extrema. The graph tends to toward -8 but that is not a minimum.