### Home > APCALC > Chapter 3 > Lesson 3.3.2 > Problem 3-109

Curves can be labeled with descriptors such as “concave down” and “increasing.” On graph paper, graph each function and label its respective parts. Use different colors to represent concavity.

**Curve Analysis**

A function is **increasing **on an interval if increases as

*increases. Likewise, a function is*

**decreasing**on an interval if

*decreases as*

*increases.*

One way to determine if a function is increasing or decreasing is to determine the domain on which the slope of its tangent lines,

For example give

The coordinate point where a function changes from increasing to decreasing or vice versa is called an **extrema**. This extreme point is either a **maximum** or a **minimum**. The function graphed at right has extrema at and

*.*

Note: If a function is increasing or decreasing over its entire domain, the function is **monotonic**.

When the *slopes of the tangent lines* increase on an interval, the graph is **concave up** because it curves up. However, when the slopes decrease on an interval, the graph is **concave down **because it curves down.The graph of , shown above, is concave up for

A coordinate point where the concavity changes is called a **point of inflection**. At this point, the curve changes from concave up to concave down or vice versa.