CPM Homework Help : CALC Problem 4-91

Compute without a calculator Without your calculator, describe the graph of $f(x) = x^3 + 12x^2 + 36x-6$ . A complete answer states where $f(x)$ is increasing, decreasing, concave up, concave down, and points of inflection.

Hint:

When $f^\prime(x) > 0$ , $f(x)$ is increasing. When $f^\prime(x) < 0$ , $f(x)$ is decreasing. An inflection point occurs when $f^\prime(x) = 0$ . When $f^{\prime\prime}(x) > 0$ , the function is concave up. When $f^{\prime\prime}(x) < 0$ , the function is concave down.