Chapter 3: Q. 10 (page 314)

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 .
$f (x) = x^{3} - 15 x^{2} - 33 x$

Short Answer

Expert verified

x=0,16.95,-1.95

Step by step solution

Step 1. Given Information

Consider a function

$f (x) = x^{3} - 15 x^{2} - 33 x$

Step 2. Calculation for roots

For finding roots of the function;

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

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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 .
$f (x) = x^{3} - 15 x^{2} - 33 x$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation for roots

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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(x)=x3−15x2−33x

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation for roots

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Decision Maths

Statistics

Calculus

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

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 .
$f (x) = x^{3} - 15 x^{2} - 33 x$