Checkpoint: Increasing and Decreasing Intervals Solution

Name the interval(s) in which the function increases and decreases.

$g (x) = x^{2} (2 x - 1) (x + 1.75)$

Increases across the intervals $(- 1.279, 0)$ and $(0.342, + \infty)$

Decreases across the intervals $(- \infty, - 1.279)$ and $(0, 0.342)$

Note

Use technology to view the function. Creating a sketch is optional but can be helpful as a reference.

Q: What information do you need from a graph to determine increasing and decreasing intervals?
A: The turning points

Q: Is it possible for a root to also be a turning point? Explain.

A: Yes. For example, a bounce (multiplicity 2) is a root and a turning point.