The Natural Exponential Function

Definition The inverse function of the natural logarithmic function f(x) = ln x is called the natural exponential function and is denoted by f -1 (x) = e x y = e x if and only if x = ln y ln(e x ) = x e lnx = x

Properties of Natural Exponential Functions 1) The domain of f(x) = e x is (-∞, ∞) and the range is (0, ∞) 2) The function is continuous, increasing, and one-to- one on its entire domain 3) The graph is concave upward on its entire domain 4) and

Operations with Exponential Functions

Example 1) 2)

Derivatives of Natural Exponential

Examples 1) 2) 3)

4) Find the relative extrema of