There is three ways of a function f with its derivative of the function be greater than 0 can be appear in a graph.

All of them shows the function f increases on the graph…

What is the difference?

(tells how the slopes of f changes) The slope (derivative) of f’(x) Particle Motion

• One increases the rate [f’(x)] of how the graph is increasing. (concave up)
  • f’’(x)>0
• One states that the rate [f’(x)] of how the graph is remain constant (no concavity)
  • f’’(x)=0
• One decreases the rate [f’(x)] of how the graph is increasing (concave down)
  • f’’(x)<0

Inflection Value and Points with Theorem

Second Derivative Test