### 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. Homework Help ✎

**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.