7th Edition

ISBN: 9781337291248

Author: Waner, Stefan.

Publisher: Cengage Learning,

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 …

Videos

Textbook Question

Chapter 4, Problem 57RE

Sales OHaganBooks.com fits the cubic curve

w ( t ) = − 3.7 t 3 + 74.6 t 2 + 135.5 t + 6 , 300 ( 0 ≤ t ≤ 6 )

to its weekly sales figures (see Chapter 3 Review Exercise 57; t is time in weeks), as shown in the following graph:

Chapter 4, Problem 57RE, Sales OHaganBooks.com fits the cubic curve w(t)=3.7t3+74.6t2+135.5t+6,300(0t6) to its weekly sales

Week

a. According to the cubic model, what was the rate of increase of sales at the beginning of the second week ( t = 1 ) ? (Round your answer to the nearest unit.)

b. If we extrapolate the model, what would be the rate of increase of weekly sales at the beginning of the eighth week ( t = 7 ) ?

c. Graph the function w for 0 ≤ t ≤ 20. . Would it be realistic to use the function to predict sales through week 20? Why?

d. By examining the graph, say why the choice of a quadratic model would result in radically different long- term predictions of sales.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4, Problem 56RE

Chapter 4, Problem 58RE

Students have asked these similar questions

4. Use method of separation of variable to solve the following wave equation მłu J²u subject to u(0,t) =0, for t> 0, u(л,t) = 0, for t> 0, = t> 0, at² ax²' u(x, 0) = 0, 0.01 x, ut(x, 0) = Π 0.01 (π-x), 0

Solve the following heat equation by method of separation variables: ди = at subject to u(0,t) =0, for -16024 ძx2 • t>0, 0 0, ux (4,t) = 0, for t> 0, u(x, 0) = (x-3, \-1, 0 < x ≤2 2≤ x ≤ 4.

ex 5. important aspects. Graph f(x)=lnx. Be sure to make your graph big enough to easily read (use the space given.) Label all 6 33

Chapter 4 Solutions

Applied Calculus

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.

Solution Summary: The author calculates the rate of increase of sales at the start of the second week if the sales of OHaganBooks.com fits the cubic curve.

Concept explainers

Videos

Want to see the full answer?

Chapter 4 Solutions