### Home > CALC > Chapter 6 > Lesson 6.5.1 > Problem 6-171

6-171.

Thoroughly investigate the graph of . Identify all important qualities, such as where the function is increasing, decreasing, concave up, and concave down. Also identify any point(s) of inflection and intercepts, and provide graphs of

*and*

*. Be sure to justify all statements both*

*graphically*and

*analytically*.

Remember to investigate all extrema CANDIDATES. That means, find all values of where

*AND*

*f*'(

*x*) DNE.

After all, a max or min could exist at a cusp... But remember, sometimes these candidates turn out to be inflection points instead.

When looking for points of inflection, remember to consider where concavity changes. This could happen where

or where DNE.