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Find average and instantaneous rates of change. Understand the instantaneous rate of change as the limit of the average rate of change. Interpret a derivative as a rate of change in applications, including velocity, speed, and acceleration.
Remarks
Example: The vertical distance traveled by an object within the earth’s gravitational field (and neglecting air resistance) is given by the equation
, where g is the force on the object due to earth’s gravity, Vo is the initial velocity, Xo is the initial height above the ground, t is the time in seconds, and down is the negative vertical direction. Determine the instantaneous speed and the average speed for an object, initially at rest, 3 seconds after it is dropped from a 100m tall cliff. What about 5 seconds after?. Use 
.
General Information
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Calculus
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Applications of Derivatives - Apply knowledge about derivatives to find slopes of curves and the related tangent lines. Analyze and graph functions, finding where they are increasing or decreasing, their maximum and minimum points, their points of inflection, and their concavity. Solve optimization problems, find average and instantaneous rates of change (including velocities and accelerations), and model rates of change. Find slopes and equations of tangent lines, maximum and minimum points, and points of inflection. Solve optimization problems, and find rates of change.
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))
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