Graph Functions with Given Characteristics

This objective is a review of previous objectives.

Intervals of Increase or Decrease

The notation f'(x) > 0 ("f-prime of x" or the derivative of the function) describes the portion of the function that is increasing or going up—where y values increase as the x value increases.

The notation f'(x) < 0 describes the portion of the function that is decreasing or going down.

Concavity

The notation f''(x) > 0 ("f-double-prime of x" or the second derivative of the function) describes the portion of the graph that is concave upward.

The notation f''(x) < 0 describes the portion of the graph that is concave downward.