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State, understand, and apply the definition of derivative.
Remarks
Example 1 (related to the example given in C.2.1):Find
. What does the result tell you?Use the limit given above to determine the derivative function for f(x). In other words calculate f ’(x) =
for 
.Example 2: For the function g(x), shown on the graph, draw the graph of g’(x) by estimation. Explain how you arrived at your solution.
Example 3: The graph of the function f(x) is given below. Find a function g(x) such that the derivative of g(x) will be f(x). Explain your solution.
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
-
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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Tutorials
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
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