Explanation Given: The function is f ( x ) = x 3 + 3 x 2 − 3 . Formula Used: If f function, then a number c for which f ( c ) is defined and e i t h e r f ' ( 0 ) = 0 . The function f is said to have a local extremum at c if it has a local maximum or minimum there. If f has local extremum at x = c , then c is a critical number of f . Calculation: Consider the provided function: f ( x ) = x 3 + 3 x 2 − 3 Differentiate the function with respect to x . f ′ ( x ) = 3 x 2 + 3 ( 2 x ) = 3 x 2 + 6 x Solve for f ′ ( x ) = 0 to find the critical points. 3 x 2 + 6 x = 0 3 x ( x + 2 ) = 0 Further solve. 3 x = 0 x = 0 Or, x + 2 = 0 x = − 2 Use the first derivative test. Take points as x = − 2.5 , x = − 0

12th Edition

ISBN: 9780135240687

Author: Lial

Publisher: PEARSON

See similar textbooks

Concept explainers

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, c…

Videos

Question

Chapter 12.1, Problem 19E

To determine

To calculate: the location of local extremum of given function, f(x)=x3+3x2−3.

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 20E

Students have asked these similar questions

Please could you provide a step by step solutions to this question and explain every step.

Could you please help me with question 2bii. If possible could you explain how you found the bounds of the integral by using a graph of the region of integration. Thanks

Let A be a vector space with basis 1, a, b. Which (if any) of the following rules turn A into an algebra? (You may assume that 1 is a unit.) (i) a² = a, b² = ab = ba = 0. (ii) a²=b, b² = ab = ba = 0. (iii) a²=b, b² = b, ab = ba = 0.

Chapter 12 Solutions

MATHEMATICS WITH APPL....-ACCESS

Ch. 12.1 - Checkpoint 1 For what values of x is the function...Ch. 12.1 - Checkpoint 2 Find all intervals on which is...Ch. 12.1 - Checkpoint 3 Identity the x-values of all points...Ch. 12.1 - Checkpoint 4 Find the critical numbers for each of...Ch. 12.1 - Prob. 5CP Ch. 12.1 - Prob. 6CP Ch. 12.1 - Checkpoint 7 Find the locations of the local...Ch. 12.1 - Prob. 8CP Ch. 12.1 - Checkpoint 9 If a sales function is given by...Ch. 12.1 - Prob. 1E

Knowledge Booster

Learn more about

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

the location of local extremum of given function, f ( x ) = x 3 + 3 x 2 − 3 .

Concept explainers

Videos

To calculate: the location of local extremum of given function, f(x)=x3+3x2−3.

Want to see the full answer?

Chapter 12 Solutions