Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Question

Chapter 5.2, Problem 57E

(a)

To determine

To find: The find the region where the f is increasing, decreasing or has the local extrema.

(a)

Expert Solution

Answer to Problem 57E

The region where the f is increasing, decreasing or has the local extrema is obtained.

Explanation of Solution

Given:

The given table is shown in Table 1

Table 1

x	f′(x)	x	f′(x)
-2	7	0.25	4.81
-1.75	4.19	0.5	-4.25
-1.5	1.75	0.75	-3.31
-1.25	-0.31	1	-2
-1	-2	1.25	-0.31
-0.75	-3.31	-1.5	1.75
-0.5	-4.25	1.75	4.19
-0.25	-4.81	2	7
0	-5

Calculation:

The graph for the values given in the table is shown in Figure 1

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 5.2, Problem 57E

Figure 1

Consider that the f is continuous on [−2,2] and differentiable at (−2,2) .

Then, if the function has the maximum value or the local minimum value at the interior point c of the domain and if f′ exists at c then f′(c)=0 .

Consider that f is continuous on [a,b] and it is differentiable at (a,b) .

Consider that f′>0 is continuous on [a,b] and it is differentiable at [a,b] .

Consider that f′<0 is continuous on [a,b] and it is differentiable at [a,b] .

Consider that for the given table x=−2 to −1.5 then the value of f′(x) is positive and the curve meets the x axis at the points x=−1.3 .

From this it is clear that the function increases on the interval [1.3,1.3] .

Consider that for the given table x=−1.25 to 1.25 then the value of f′(x) is negative and the curve meets the x axis at the points x=−1.3 and x=1.3 .

From this it is clear that the function decrease on the interval [−1.3,1.3] .

Thus, the local maxima for the given function is at x=1.3 and the minima is at x=−1.3 .

(b)

To determine

To find: The quadratic regression of the equation for the data in the table and superimpose the graph on the scatter plot of the data.

(b)

Expert Solution

Answer to Problem 57E

The required regression equation is y=3x2−5 and the regression line on the graph is shown in Figure 1

Explanation of Solution

Calculation:

From the table 1 when the values are entered in the calculator the regression equation is obtained as,

y=3x2−5

(c)

To determine

To find: The formula for the f that satisfies the f(0)=0 .

(c)

Expert Solution

Answer to Problem 57E

The function is f(x)=x3−5x .

Explanation of Solution

Calculation:

Consider the regression equation is,

y=3x2−5

Then,

f(x)=x3−5x+Cf(0)=(0)3−5(0)+CC=0

Then the function is f(x)=x3−5x .

Chapter 5.2, Problem 56E

Chapter 5.2, Problem 58E

Chapter 5 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 5.1 - Prob. 1QR Ch. 5.1 - Prob. 2QR Ch. 5.1 - Prob. 3QR Ch. 5.1 - Prob. 4QR Ch. 5.1 - Prob. 5QR Ch. 5.1 - Prob. 6QR Ch. 5.1 - Prob. 7QR Ch. 5.1 - Prob. 8QR Ch. 5.1 - Prob. 9QR Ch. 5.1 - Prob. 10QR

Ch. 5.1 - Prob. 11QR Ch. 5.1 - Prob. 12QR Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - 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