Explanation Given Information: The provided equation is: g ( x ) = x 3 − 12 x Calculation: Consider the provided equation: g ( x ) = x 3 − 12 x Differentiate both sides of the above equation with respect to x , g ′ ( x ) = 3 x 2 − 12 Locating stationary points: Stationary Points: Points in the interior of the domain where the derivative of the function is zero. To locate stationary points set g ′ ( x ) = 0 and solve for x . So, g ′ ( x ) = 0 3 x 2 − 12 = 0 Add 12 to both sides of the equation: 3 x 2 − 12 = 0 3 x 2 − 12 + 12 = 12 3 x 2 = 12 Multiply both sides of the equation by 1 3 to get: 3 x 2 = 12 3 x 2 1 3 = 12 1 3 x 2 = 4 Take square root both sides of the above equation to get: x 2 = 4 x 2 = ± 4 x = ± 2 The domain of the function is [ − 4 , 4 ] , so x = ± 2 is in the interior of the domain. Thus, the only candidate for a stationary relative extremum occurs when x = ± 2 . Locating Singular points: Singular Points: Points in the interior of the domain where the derivative of the function is not defined. To locate singular points, find the interior points x where g ′ ( x ) is not defined but g ( x ) is defined. Since g ′ ( x ) is defined for all x in the interior of the domain, so there are no singular points

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

Videos

Question

Chapter 12.1, Problem 15E

To determine

To calculate: The exact location of the relative and absolute extrema of the function g(x)=x3−12x with domain [−4,4].

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.1, Problem 14E

Chapter 12.1, Problem 16E

Students have asked these similar questions

This question is a previous exam question. I am using it for practice but am stuck

in Q. A firm price of 501: If the Total cast is given by perfect competition sells its products at the TTC = 3Q² +2Q+5. level of output will will be the level of profit at What What Devive the Consumer Curve approach. demand the function maximize this firm's, that using putput level. the indifference prpfit. Q₂. The Total Cost equation in the production of bacon has hypothetical factor a 2 A C= "TC 1000+ 159" +03 ; Where ç. Kash, Bacao - metric bone Compute and 11" tonnes the and average cost at output level of 10. Stretch theme marginal cost of the the shope Carve an the production average, Cost arve 12 tonnes and explain, the relationship between Marginal Cost product es tamen op d Galaxy A71 01 Curve in

if w(x, y, z) = sin' ( xyz) (y zî + x z j + xy k) Find grad (div) at (0.5, 1, 0.5) (xyz)2

Chapter 12 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The exact location of the relative and absolute extrema of the function g ( x ) = x 3 − 12 x with domain [ − 4 , 4 ] .

Solution Summary: The author explains how to calculate the exact location of the relative and absolute extrema of a function.

Concept explainers

Videos

To calculate: The exact location of the relative and absolute extrema of the function g(x)=x3−12x with domain [−4,4].

Want to see the full answer?

Chapter 12 Solutions