### Home > APCALC > Chapter 4 > Lesson 4.2.4 > Problem4-88

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.

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.