Question

Find all roots, local maxima and minima, and inflection points of each function f . In addition, determine whether any local extrema are also global extrema on the domain of f .

$f\left(x\right)=x^3-15x^2-33x$

Short answer

x=0,16.95,-1.95

Step-by-step solution

Step 1. Given Information

Consider a function

$f\left(x\right)=x^3-15x^2-33x$

Step 2. Calculation for roots

For finding roots of the function;

$\begin{array}{c}f\left(x\right)=0\\ x^3-15x^2-33x=0\\ x\left(x^2-15x-33\right)=0\\ \text{Either}x=0\text{or}{x}^2-15x-33=0\\ x=0\text{or}x=\frac{15\pm \sqrt{(-15{)}^2-4\cdot 1\cdot (-33)}}{2\cdot 1}\\ x=0\text{or}x=\frac{15\pm \sqrt{255+132}}{2}\\ x=0\text{or}x=\frac{15\pm \sqrt{357}}{2}\\ x=0,16.95,-1.95\end{array}$