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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: Level 3: Strategic Thinking & Complex Reasoning
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
This benchmark is part of these courses.
1202300: Calculus Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
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Related Resources
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Tutorials
Video/Audio/Animation
Virtual Manipulative
Student Resources
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Tutorials
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.
Type: Tutorial
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.
Type: Tutorial
Derivative as Slope of a Tangent Line:
We will find the derivative of a function by finding the slope of the tangent line.
Type: Tutorial
Mean Value Theorem:
In this video we will take an in depth look at the Mean Value Theorem.
Type: Tutorial
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.
Type: Tutorial
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.
Type: Tutorial
Parent Resources
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