Problem 19a
Page 280
Section 4.3: Derivatives and Shapes of Curves
Chapter 4: Applications of Differentiation
Given information
Given the function 
is continuous on 
and 
.
The characteristics of the function 
are to be analysed.
Step-by-step explanation
For a continuous function at any given point if the first derivative is:
1. greater than 0, then the function is increasing at the point
2. less than 0, then the function is decreasing at the point
3. equals 0, then the function has a critical point.
For a continuous function at any given point if the second derivative is:
1. greater than 0, then the graph is concave up at the point
2. less than 0, then the graph is concave down at the point
3. equals 0, then the function has an inflection point.
And at critical point, if the second derivative is positive then the function has a local minimum at that point and if the second derivative is negative then the function has a local maximum at that point.
Single Variable Calculus: Early Transcendentals
Solutions
Chapter
Section
- Problem 1
- Problem 2
- Problem 2a
- Problem 2b
- Problem 2c
- Problem 3
- Problem 3a
- Problem 3b
- Problem 3c
- Problem 4
- Problem 4a
- Problem 4b
- Problem 5a
- Problem 5b
- Problem 5c
- Problem 6a
- Problem 6b
- Problem 6c
- Problem 6d
- Problem 7a
- Problem 7b
- Problem 7c
- Problem 8a
- Problem 8b
- Problem 8c
- Problem 9a
- Problem 9b
- Problem 9c
- Problem 10a
- Problem 10b
- Problem 10c
- Problem 11a
- Problem 11b
- Problem 11c
- Problem 12a
- Problem 12b
- Problem 12c
- Problem 13a
- Problem 13b
- Problem 13c
- Problem 14a
- Problem 14b
- Problem 14c
- Problem 15a
- Problem 15b
- Problem 15c
- Problem 16a
- Problem 16b
- Problem 16c
- Problem 17
- Problem 18
- Problem 19a
- Problem 19b
- Problem 20a
- Problem 20b
- Problem 21a
- Problem 21b
- Problem 21c
- Problem 21d
- Problem 22a
- Problem 22b
- Problem 22c
- Problem 22d
- Problem 23a
- Problem 23b
- Problem 23c
- Problem 23d
- Problem 24a
- Problem 24b
- Problem 24c
- Problem 24d
- Problem 25a
- Problem 25b
- Problem 25c
- Problem 25d
- Problem 26a
- Problem 26b
- Problem 26c
- Problem 26d
- Problem 27a
- Problem 27b
- Problem 27c
- Problem 27d
- Problem 28a
- Problem 28b
- Problem 28c
- Problem 28d
- Problem 29a
- Problem 29b
- Problem 29c
- Problem 29d
- Problem 30a
- Problem 30b
- Problem 30c
- Problem 30d
- Problem 31a
- Problem 31b
- Problem 31c
- Problem 31d
- Problem 32a
- Problem 32b
- Problem 32c
- Problem 32d
- Problem 33a
- Problem 33b
- Problem 33c
- Problem 33d
- Problem 33e
- Problem 34a
- Problem 34b
- Problem 34c
- Problem 34d
- Problem 34e
- Problem 35a
- Problem 35b
- Problem 35c
- Problem 35d
- Problem 35e
- Problem 36a
- Problem 36b
- Problem 36c
- Problem 36d
- Problem 36e
- Problem 37a
- Problem 37b
- Problem 37c
- Problem 37d
- Problem 37e
- Problem 38a
- Problem 38b
- Problem 38c
- Problem 38d
- Problem 38e
- Problem 39a
- Problem 39b
- Problem 39c
- Problem 39d
- Problem 39e
- Problem 40a
- Problem 40b
- Problem 40c
- Problem 40d
- Problem 40e
- Problem 41
- Problem 42
- Problem 43a
- Problem 43b
- Problem 44a
- Problem 44b
- Problem 45a
- Problem 45b
- Problem 46a
- Problem 46b
- Problem 47
- Problem 48
- Problem 49a
- Problem 49b
- Problem 49c
- Problem 49d
- Problem 50a
- Problem 50c
- Problem 51
- Problem 52
- Problem 53
- Problem 54
- Problem 55
- Problem 56
- Problem 57
- Problem 58a
- Problem 58b
- Problem 58c
- Problem 59
- Problem 60
- Problem 61
- Problem 62a
- Problem 62b
- Problem 62c
- Problem 63
- Problem 64
- Problem 65
- Problem 66
- Problem 67
- Problem 68
- Problem 69
- Problem 70
- Problem 71a
- Problem 71b
- Problem 72