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  3. ZuAI AP College Board Calculus AB/BC
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Analytical Applications of Differentiation

Abigail Young

Abigail Young

11 min read

Next Topic - Using the Mean Value Theorem
Study Guide Overview

This study guide covers applying differentiation, focusing on graphical analysis and key theorems. Topics include the Mean Value Theorem (MVT), Extreme Value Theorem (EVT), and finding local and global extrema using the First and Second Derivative Tests and the Candidates Test. Additionally, it covers determining function concavity, inflection points, sketching graphs of functions and their derivatives, and solving optimization problems.

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Previous Topic - Using L'Hopitals Rule for Determining Limits in Indeterminate FormsNext Topic - Using the Mean Value Theorem

Question 1 of 10

Which of the following conditions MUST be met for the Mean Value Theorem to apply to a function f(x)f(x)f(x) on an interval [a,b][a, b][a,b]? 🤔

f(x)f(x)f(x) must be continuous on the open interval (a,b)(a, b)(a,b) and differentiable on the closed interval [a,b][a, b][a,b]

f(x)f(x)f(x) must be differentiable on the closed interval [a,b][a, b][a,b]

f(x)f(x)f(x) must be continuous on the closed interval [a,b][a, b][a,b] and differentiable on the open interval (a,b)(a, b)(a,b)

f(x)f(x)f(x) must be differentiable on the open interval (a,b)(a, b)(a,b)