CPM Homework Help : APCALC Problem 4-88

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

Hint:

When $f^\prime(x) > 0$ , $f(x)$ is increasing. When $f^\prime(x) < 0$ , $f\left(x\right)$ 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.

Compute without a calculator