Standard #: MAFS.912.C.2.10 (Archived Standard)


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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
Date of Last Rating: 02/14
Status: State Board Approved - Archived

Related Courses

Course Number1111 Course Title222
1202300: Calculus Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))


Related Resources

Tutorials

Name Description
Mean Value Theorem

We will learn the meaning of the Mean Value Theorem.

Mean Value Theorem

In this video we will take an in depth look at the Mean Value Theorem.

Student Resources

Tutorials

Name Description
Mean Value Theorem:

We will learn the meaning of the Mean Value Theorem.

Mean Value Theorem:

In this video we will take an in depth look at the Mean Value Theorem.



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