Standard #: MAFS.912.C.2.1 (Archived Standard)


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Understand the concept of derivative geometrically, numerically, and analytically, and interpret the derivative as an instantaneous rate of change or as the slope of the tangent line.


Remarks


Example: Approximate the derivative of  at x=5 by calculating values of  for values of h that are very close to zero. Use a diagram to explain what you are doing and what the result means.

General Information

Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Calculus
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 3: Strategic Thinking & Complex Reasoning - More Information
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
Calculus: Derivatives 1

In this video we will learn through an example, that a derivative is simply the slope of a curve at any given point.

Calculating Slope of Tangent Line Using Derivative Definition

In this video we will find the slope of the tangent line using the formal definition of derivative.

Mean Value Theorem

We will learn the meaning of the Mean Value Theorem.

Derivative as Slope of a Tangent Line

We will find the derivative of a function by finding the slope of the tangent line.

Mean Value Theorem

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

The Derivative of f(x)=x^2 for Any x

In this video we will find the derivative of a function based on the slope of the tangent line.

Chain Rule Example Using Visual Information

In this video we will analyze the graph of a function and its tangent line, then use the chain rule to find the value of the derivative at that point.

Video/Audio/Animation

Name Description
MIT BLOSSOMS - The Physics of Boomerangs

This learning video explores the mysterious physics behind boomerangs and other rapidly spinning objects. Students will get to make and throw their own boomerangs between video segments! A key idea presented is how torque causes the precession of angular momentum. One class period is required to complete this learning video, and the optimal prerequisites are a familiarity with forces, Newton's laws, vectors and time derivatives. Each student would need the following materials for boomerang construction: cardboard (roughly the size of a postcard), ruler, pencil/pen, scissors, protractor, and a stapler.

Virtual Manipulative

Name Description
Derivative Plotter

This online applet that depicts the derivative of a given function. Can use demo examples or a user-defined function.

Student Resources

Tutorials

Name Description
Calculus: Derivatives 1:

In this video we will learn through an example, that a derivative is simply the slope of a curve at any given point.

Calculating Slope of Tangent Line Using Derivative Definition:

In this video we will find the slope of the tangent line using the formal definition of derivative.

Mean Value Theorem:

We will learn the meaning of the Mean Value Theorem.

Derivative as Slope of a Tangent Line:

We will find the derivative of a function by finding the slope of the tangent line.

Mean Value Theorem:

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

The Derivative of f(x)=x^2 for Any x:

In this video we will find the derivative of a function based on the slope of the tangent line.

Chain Rule Example Using Visual Information:

In this video we will analyze the graph of a function and its tangent line, then use the chain rule to find the value of the derivative at that point.



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