Half-exponential function: Difference between revisions

Revision as of 03:19, 18 March 2024

Revision as of 16:40, 15 August 2024

Line 18:

[[File:Half-exponential_function.png|thumb|right|300px|Example of a half-exponential function]]

A simple example, which leads to <math>f</math> having a continuous first derivative <math>f'</math> everywhere, isand toalso takecauses
<math>A=f''\tfrac12ge 0</math> andeverywhere (i.e. <math>gf(x)=x+\tfrac12</math>, givingis concave-up,

and <math>f'(x)</math> increasing,

for all <math>x\gt 0</math>),

is to take <math>A=\tfrac12</math> and <math>g(x)=x+\tfrac12</math>, giving

<math display=block> f (x) =

\begin{cases}