How derivatives reveal the hidden direction of a function
In short: Understanding why a graph climbs or falls requires more than just looking at it. This video explains how to use calculus to provide a rigorous justification for a function's behavior.
The core concept involves using the derivative, f', to explain properties of an original function, f. Specifically, students learn how to justify why a function is increasing by analyzing its rate of change.
The lesson features Bill Scott, a member of the team that helped develop Khan Academy's AP lessons. He demonstrates correct methods for these justifications while highlighting common pitfalls to avoid in calculus examinations.
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Sources
- Summary by Intellect · source: Calculus based justification for function increasing | AP Calculus AB | Khan Academy
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