7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

Concept explainers

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 …

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Question

Chapter 4.3, Problem 12PS

(a)

To determine

The critical points of f(x)=x3+3x2+1

(b)

To determine

The intervals where f(x)=x3+3x2+1 is increasing or decreasing.

(c)

To determine

The relative maxima, relative minima or neither.

(d)

To determine

Second order critical points and intervals for concavity

(e)

To determine

Graph of function f(x)=x3+3x2+1

Expert Solution & Answer

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Chapter 4.3, Problem 11PS

Chapter 4.3, Problem 13PS

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Chapter 4 Solutions

Calculus

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The critical points of f ( x ) = x 3 + 3 x 2 + 1

Solution Summary: The author explains the critical points of f(x)=x3+3x2+1 and the sign of its derivative.

Concept explainers

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The critical points of f(x)=x3+3x2+1

The intervals where f(x)=x3+3x2+1 is increasing or decreasing.

The relative maxima, relative minima or neither.

Second order critical points and intervals for concavity

Graph of function f(x)=x3+3x2+1

Want to see the full answer?

Chapter 4 Solutions