### Home > CALC > Chapter 4 > Lesson 4.2.4 > Problem 4-91

4-91.

*Without your calculator*, describe the graph of *f*(*x*) =* x*^{3} + 12*x*^{2} + 36*x *− 6. A complete answer states where *f*(*x*) is increasing, decreasing, concave up, concave down, and points of inflection. Homework Help ✎

When *f* '(*x*) > 0, *f*(*x*) is increasing. When *f* '(*x*) < 0, *f*(*x*) is decreasing. An inflection point occurs when *f* '(*x*) = 0. When *f* ''(*x*) > 0, the function is concave up. When *f* ''(*x*) < 0, the function is concave down.