To define: The second derivative of function f.
Explanation of Solution
(1) The second derivative is derivative of the derivative function.
(2) The second derivative exhibits whether a point with zero is critical point.
Case (i):
The second derivative is negative for the maximum point. The slope of the curve is at first positive, then goes through zero to become negative.
Case (ii):
The second derivative is positive for the minimum point. The slope of the curve is at first negative, then goes through zero to become positive.
Case (iii):
The second derivative and first derivative both are zero for the inflexion point at same time. It represents a point where the curvature is changing its sense. Inflexion points are relatively rare.
Chapter 2 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning