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Understand and use the relationship between differentiability and continuity.
Remarks
Example 1: Let f(x)=1/x. Is f(x) continuous at x = 0? Is f(x) differentiable at x = 0? Explain your answers.Example 2: Is f(x) = IxI continuous at x=0? Is f(x) differentiable at x=0? Explain your answers.
General Information
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Calculus
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Differential Calculus - Develop an understanding of the derivative as an instantaneous rate of change, using geometrical, numerical, and analytical methods. Use this definition to find derivatives of algebraic and transcendental functions and combinations of these functions (using, for example, sums, composites, and inverses). Find second and higher order derivatives. Understand and use the relationship between differentiability and continuity. Understand and apply the Mean Value Theorem. Find derivatives of algebraic, trigonometric, logarithmic, and exponential functions. Find derivatives of sums, products, and quotients, and composite and inverse functions. Find derivatives of higher order, and use logarithmic differentiation and the Mean Value Theorem.
Date Adopted or Revised: 02/14
Content Complexity Rating:
Level 2: Basic Application of Skills & Concepts
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More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Related Courses
This benchmark is part of these courses.
1202300: Calculus Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
Related Access Points
Alternate version of this benchmark for students with significant cognitive disabilities.
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Tutorials
Student Resources
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Tutorials
Mean Value Theorem:
In this video we will take an in depth look at the Mean Value Theorem.
Type: Tutorial
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