The definition of e
Among all exponential functions of the form , one of them has a particularly nice property. When the base of the exponent, , is approximately 2.71828, the line tangent to the graph of at has slope 1. Use the interactive figure below to confirm this. (You can use the arrow keys on your keyboard for fine adjustment of the slider.)
The exact value for that produces a tangent line of slope 1 is the famous number . In fact, this is one way that can be defined.