## Calculus: Graphical, Numerical, Algebraic, 3rd Edition Answers Ch 3 Derivatives Ex 3.4

Chapter 3 Derivatives Exercise 3.4 1E

Chapter 3 Derivatives Exercise 3.4 1QR

Chapter 3 Derivatives Exercise 3.4 2E

Chapter 3 Derivatives Exercise 3.4 2QR

Chapter 3 Derivatives Exercise 3.4 3E

Chapter 3 Derivatives Exercise 3.4 3QR

Chapter 3 Derivatives Exercise 3.4 4E

Chapter 3 Derivatives Exercise 3.4 4QR

Chapter 3 Derivatives Exercise 3.4 5E

Chapter 3 Derivatives Exercise 3.4 5QR

Chapter 3 Derivatives Exercise 3.4 6E

Chapter 3 Derivatives Exercise 3.4 6QR

Chapter 3 Derivatives Exercise 3.4 7E

Chapter 3 Derivatives Exercise 3.4 7QR

Chapter 3 Derivatives Exercise 3.4 8E

Chapter 3 Derivatives Exercise 3.4 8QR

Chapter 3 Derivatives Exercise 3.4 9E

Chapter 3 Derivatives Exercise 3.4 9QR

Chapter 3 Derivatives Exercise 3.4 10E

Chapter 3 Derivatives Exercise 3.4 10QR

Chapter 3 Derivatives Exercise 3.4 11E

Chapter 3 Derivatives Exercise 3.4 12E

(d) The horse is running the fastest during the last furlong (between 9th and 10th furlong markers). This furlong takes only 11 seconds to run, which is the least amount of time for a furlong.
(e) The horse accelerates the fastest during the first furlong (between markers 0 and 1) because horse starts with zero speed and reaches to a great speed so the rate of change of speed is largest during the first furlong.

Chapter 3 Derivatives Exercise 3.4 13E

Chapter 3 Derivatives Exercise 3.4 14E

Chapter 3 Derivatives Exercise 3.4 15E

Chapter 3 Derivatives Exercise 3.4 16E

Chapter 3 Derivatives Exercise 3.4 17E

Chapter 3 Derivatives Exercise 3.4 18E

Chapter 3 Derivatives Exercise 3.4 19E

Chapter 3 Derivatives Exercise 3.4 20E

Chapter 3 Derivatives Exercise 3.4 21E

Chapter 3 Derivatives Exercise 3.4 22E

Chapter 3 Derivatives Exercise 3.4 23E

Chapter 3 Derivatives Exercise 3.4 24E

Chapter 3 Derivatives Exercise 3.4 25E

Chapter 3 Derivatives Exercise 3.4 26E

Chapter 3 Derivatives Exercise 3.4 27E

Chapter 3 Derivatives Exercise 3.4 28E

Chapter 3 Derivatives Exercise 3.4 29E

Chapter 3 Derivatives Exercise 3.4 30E

Chapter 3 Derivatives Exercise 3.4 31E
In the given figure graph C is position, graph A is velocity and graph B is acceleration. Because A is the derivative of C as we see that it is positive, negative and zero where C is increasing, decreasing and has horizontal tangents, respectively. The relationship between B and A is similar.

Chapter 3 Derivatives Exercise 3.4 32E

Chapter 3 Derivatives Exercise 3.4 33E

Chapter 3 Derivatives Exercise 3.4 34E

Chapter 3 Derivatives Exercise 3.4 35E

Chapter 3 Derivatives Exercise 3.4 36E

Chapter 3 Derivatives Exercise 3.4 37E

Chapter 3 Derivatives Exercise 3.4 38E

Chapter 3 Derivatives Exercise 3.4 39E

Chapter 3 Derivatives Exercise 3.4 40E

Chapter 3 Derivatives Exercise 3.4 41E

Chapter 3 Derivatives Exercise 3.4 42E

Chapter 3 Derivatives Exercise 3.4 43E

Chapter 3 Derivatives Exercise 3.4 44E

Chapter 3 Derivatives Exercise 3.4 45E

Chapter 3 Derivatives Exercise 3.4 46E

Chapter 3 Derivatives Exercise 3.4 47E

Chapter 3 Derivatives Exercise 3.4 48E

Chapter 3 Derivatives Exercise 3.4 49E

Chapter 3 Derivatives Exercise 3.4 50E

## Calculus: Graphical, Numerical, Algebraic, 3rd Edition Answers Ch 3 Derivatives Ex 3.3

Chapter 3 Derivatives Exercise 3.3 1E

Chapter 3 Derivatives Exercise 3.3 1QQ

Chapter 3 Derivatives Exercise 3.3 1QR

Chapter 3 Derivatives Exercise 3.3 2E

Chapter 3 Derivatives Exercise 3.3 2QQ

Chapter 3 Derivatives Exercise 3.3 2QR

Chapter 3 Derivatives Exercise 3.3 3E

Chapter 3 Derivatives Exercise 3.3 3QQ

Chapter 3 Derivatives Exercise 3.3 3QR

Chapter 3 Derivatives Exercise 3.3 4E

Chapter 3 Derivatives Exercise 3.3 4QQ

Chapter 3 Derivatives Exercise 3.3 4QR

Chapter 3 Derivatives Exercise 3.3 5E

Chapter 3 Derivatives Exercise 3.3 5QR

Chapter 3 Derivatives Exercise 3.3 6E

Chapter 3 Derivatives Exercise 3.3 6QR

Chapter 3 Derivatives Exercise 3.3 7E

Chapter 3 Derivatives Exercise 3.3 7QR

Chapter 3 Derivatives Exercise 3.3 8E

Chapter 3 Derivatives Exercise 3.3 8QR

Chapter 3 Derivatives Exercise 3.3 9E

Chapter 3 Derivatives Exercise 3.3 9QR

Chapter 3 Derivatives Exercise 3.3 10E

Chapter 3 Derivatives Exercise 3.3 10QR

Chapter 3 Derivatives Exercise 3.3 11E

Chapter 3 Derivatives Exercise 3.3 12E

Chapter 3 Derivatives Exercise 3.3 13E

Chapter 3 Derivatives Exercise 3.3 14E

Chapter 3 Derivatives Exercise 3.3 15E

Chapter 3 Derivatives Exercise 3.3 16E

Chapter 3 Derivatives Exercise 3.3 17E

Chapter 3 Derivatives Exercise 3.3 18E

Chapter 3 Derivatives Exercise 3.3 19E

Chapter 3 Derivatives Exercise 3.3 20E

Chapter 3 Derivatives Exercise 3.3 21E

Chapter 3 Derivatives Exercise 3.3 22E

Chapter 3 Derivatives Exercise 3.3 23E

Chapter 3 Derivatives Exercise 3.3 24E

Chapter 3 Derivatives Exercise 3.3 25E

Chapter 3 Derivatives Exercise 3.3 26E

Chapter 3 Derivatives Exercise 3.3 27E

Chapter 3 Derivatives Exercise 3.3 28E

Chapter 3 Derivatives Exercise 3.3 29E

Chapter 3 Derivatives Exercise 3.3 30E

Chapter 3 Derivatives Exercise 3.3 31E

Chapter 3 Derivatives Exercise 3.3 32E

Chapter 3 Derivatives Exercise 3.3 33E

Chapter 3 Derivatives Exercise 3.3 34E

Chapter 3 Derivatives Exercise 3.3 35E

Chapter 3 Derivatives Exercise 3.3 36E

Chapter 3 Derivatives Exercise 3.3 37E

Chapter 3 Derivatives Exercise 3.3 38E

Chapter 3 Derivatives Exercise 3.3 39E

Chapter 3 Derivatives Exercise 3.3 40E

Chapter 3 Derivatives Exercise 3.3 41E

Chapter 3 Derivatives Exercise 3.3 42E

Chapter 3 Derivatives Exercise 3.3 43E

Chapter 3 Derivatives Exercise 3.3 44E

Chapter 3 Derivatives Exercise 3.3 45E

Chapter 3 Derivatives Exercise 3.3 46E

Chapter 3 Derivatives Exercise 3.3 47E

Chapter 3 Derivatives Exercise 3.3 48E

Chapter 3 Derivatives Exercise 3.3 49E

Chapter 3 Derivatives Exercise 3.3 50E

Chapter 3 Derivatives Exercise 3.3 51E

Chapter 3 Derivatives Exercise 3.3 52E

Chapter 3 Derivatives Exercise 3.3 53E

Chapter 3 Derivatives Exercise 3.3 54E

Chapter 3 Derivatives Exercise 3.3 55E

Chapter 3 Derivatives Exercise 3.3 56E

Chapter 3 Derivatives Exercise 3.3 57E

Chapter 3 Derivatives Exercise 3.3 58E

Chapter 3 Derivatives Exercise 3.3 59E

## Calculus: Graphical, Numerical, Algebraic, 3rd Edition Answers Ch 3 Derivatives Ex 3.2

Chapter 3 Derivatives Exercise 3.2 1E

Chapter 3 Derivatives Exercise 3.2 1QR

Chapter 3 Derivatives Exercise 3.2 2E

Chapter 3 Derivatives Exercise 3.2 2QR

Chapter 3 Derivatives Exercise 3.2 3E

Chapter 3 Derivatives Exercise 3.2 3QR

Chapter 3 Derivatives Exercise 3.2 4E
For Left-hand derivative, function is y = x
So, left-hand derivative is given by:

Chapter 3 Derivatives Exercise 3.2 4QR

Chapter 3 Derivatives Exercise 3.2 5E
(a) Differentiable: At all the points in the interval [-3, 2].
Since, there are no any corners, cusps, vertical tangent lines, or point of discontinuity within this domain. The graph of the function is unbroken and smooth, with well defined slopes at each point.
(b) Continuous but not differentiable: None
Since the function is differentiable at all the points in the domain.
(c) Neither continuous nor differentiable: None
Since the function is differentiable at all the points in the domain; it also implies that the function is continuous at all the points in the domain interval.

Chapter 3 Derivatives Exercise 3.2 5QR

Chapter 3 Derivatives Exercise 3.2 6E
(a) Differentiable: At all the points in the interval [-2,3].
Since, there are no any corners, cusps, vertical tangent lines, or point of discontinuity within this domain. The graph of the function is unbroken and smooth, with well defined slopes at each point.
(b) Continuous but not differentiable: None
Since the function is differentiable at all the points in the domain.
(c) Neither continuous nor differentiable: None
Since the function is differentiable at all the points in the domain; it also implies that the function is continuous at all the points in the domain interval.

Chapter 3 Derivatives Exercise 3.2 6QR

Chapter 3 Derivatives Exercise 3.2 7E

Chapter 3 Derivatives Exercise 3.2 7QR

Chapter 3 Derivatives Exercise 3.2 8E

Chapter 3 Derivatives Exercise 3.2 8QR

Chapter 3 Derivatives Exercise 3.2 9E

Chapter 3 Derivatives Exercise 3.2 9QR

Chapter 3 Derivatives Exercise 3.2 10E

Chapter 3 Derivatives Exercise 3.2 10QR

Chapter 3 Derivatives Exercise 3.2 11E

Chapter 3 Derivatives Exercise 3.2 12E

Chapter 3 Derivatives Exercise 3.2 13E

Chapter 3 Derivatives Exercise 3.2 14E

Chapter 3 Derivatives Exercise 3.2 15E

Here, one-sided derivative differs from the other.
Therefore this is a problem of corner.
Hence, the problem is a corner.

Chapter 3 Derivatives Exercise 3.2 16E

Chapter 3 Derivatives Exercise 3.2 17E

Chapter 3 Derivatives Exercise 3.2 18E

Chapter 3 Derivatives Exercise 3.2 19E

Chapter 3 Derivatives Exercise 3.2 20E

Chapter 3 Derivatives Exercise 3.2 21E

Chapter 3 Derivatives Exercise 3.2 22E

Chapter 3 Derivatives Exercise 3.2 23E

Chapter 3 Derivatives Exercise 3.2 24E

Chapter 3 Derivatives Exercise 3.2 25E

Chapter 3 Derivatives Exercise 3.2 26E

Chapter 3 Derivatives Exercise 3.2 27E

Chapter 3 Derivatives Exercise 3.2 28E

Chapter 3 Derivatives Exercise 3.2 29E

Chapter 3 Derivatives Exercise 3.2 30E

Chapter 3 Derivatives Exercise 3.2 31E

Chapter 3 Derivatives Exercise 3.2 32E

Chapter 3 Derivatives Exercise 3.2 33E

Chapter 3 Derivatives Exercise 3.2 34E

Chapter 3 Derivatives Exercise 3.2 35E

Chapter 3 Derivatives Exercise 3.2 36E

Chapter 3 Derivatives Exercise 3.2 37E

Chapter 3 Derivatives Exercise 3.2 38E

Chapter 3 Derivatives Exercise 3.2 39E

Chapter 3 Derivatives Exercise 3.2 40E

Chapter 3 Derivatives Exercise 3.2 41E

Chapter 3 Derivatives Exercise 3.2 42E

Chapter 3 Derivatives Exercise 3.2 43E

Chapter 3 Derivatives Exercise 3.2 44E

Chapter 3 Derivatives Exercise 3.2 45E

Chapter 3 Derivatives Exercise 3.2 46E

Chapter 3 Derivatives Exercise 3.2 47E

Chapter 3 Derivatives Exercise 3.2 48E

## Calculus: Graphical, Numerical, Algebraic, 3rd Edition Answers Ch 3 Derivatives Ex 3.1

Chapter 3 Derivatives Exercise 3.1 1E

Chapter 3 Derivatives Exercise 3.1 1QR

Chapter 3 Derivatives Exercise 3.1 2E

Chapter 3 Derivatives Exercise 3.1 2QR

Chapter 3 Derivatives Exercise 3.1 3E

Chapter 3 Derivatives Exercise 3.1 3QR

Chapter 3 Derivatives Exercise 3.1 4E

Chapter 3 Derivatives Exercise 3.1 4QR

Chapter 3 Derivatives Exercise 3.1 5E

Chapter 3 Derivatives Exercise 3.1 5QR

Chapter 3 Derivatives Exercise 3.1 6E

Chapter 3 Derivatives Exercise 3.1 6QR

Chapter 3 Derivatives Exercise 3.1 7E

Chapter 3 Derivatives Exercise 3.1 7QR

Chapter 3 Derivatives Exercise 3.1 8E

Chapter 3 Derivatives Exercise 3.1 8QR

Chapter 3 Derivatives Exercise 3.1 9E

Chapter 3 Derivatives Exercise 3.1 9QR

Chapter 3 Derivatives Exercise 3.1 10E

Chapter 3 Derivatives Exercise 3.1 10QR

Chapter 3 Derivatives Exercise 3.1 11E

Chapter 3 Derivatives Exercise 3.1 12E

Chapter 3 Derivatives Exercise 3.1 13E

Chapter 3 Derivatives Exercise 3.1 14E

Chapter 3 Derivatives Exercise 3.1 15E

Chapter 3 Derivatives Exercise 3.1 16E

Chapter 3 Derivatives Exercise 3.1 17E

Chapter 3 Derivatives Exercise 3.1 18E

Chapter 3 Derivatives Exercise 3.1 19E

Chapter 3 Derivatives Exercise 3.1 20E

Chapter 3 Derivatives Exercise 3.1 21E

Chapter 3 Derivatives Exercise 3.1 22E

Chapter 3 Derivatives Exercise 3.1 23E

Chapter 3 Derivatives Exercise 3.1 24E

Chapter 3 Derivatives Exercise 3.1 25E

Chapter 3 Derivatives Exercise 3.1 26E

Chapter 3 Derivatives Exercise 3.1 27E

Chapter 3 Derivatives Exercise 3.1 28E

Chapter 3 Derivatives Exercise 3.1 29E

Chapter 3 Derivatives Exercise 3.1 30E

(e) We will look for the steepest part of the curve. This is where the elevation is dropping most rapidly and therefore the most likely location for significant “rapids.”
These are points where there is significant change in river elevation, causes rapid increase in the speed of the river flow and hence becomes the most dangerous section of the river.
(f) We will look for the lowest point on the graph. This is where the elevation is dropping most rapidly and therefore the most likely location for significant “rapids.”
These are points where there is significant change in depth, and hence becomes the most dangerous section of the river.

Chapter 3 Derivatives Exercise 3.1 31E

Chapter 3 Derivatives Exercise 3.1 32E

Chapter 3 Derivatives Exercise 3.1 33E

Chapter 3 Derivatives Exercise 3.1 34E

Chapter 3 Derivatives Exercise 3.1 35E

Chapter 3 Derivatives Exercise 3.1 36E

Chapter 3 Derivatives Exercise 3.1 37E

Chapter 3 Derivatives Exercise 3.1 38E

Chapter 3 Derivatives Exercise 3.1 39E

Chapter 3 Derivatives Exercise 3.1 40E

Chapter 3 Derivatives Exercise 3.1 41E

Chapter 3 Derivatives Exercise 3.1 42E

Chapter 3 Derivatives Exercise 3.1 43E

Chapter 3 Derivatives Exercise 3.1 44E

Chapter 3 Derivatives Exercise 3.1 45E