IB Class 10 Mathematics – Group 5, Calculus | 5. Maxima and Minima by Abraham | Learn Smarter
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5. Maxima and Minima

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Sections

  • 1

    Critical Points And Turning Points

    This section introduces critical points and turning points, explaining how they relate to maxima and minima in functions using derivatives.

    Learning Practice

  • 1.1

    Definition

    This section introduces the concepts of critical points and turning points in calculus, focusing on identifying maximum and minimum values of functions using derivatives.

    Learning Practice

  • 1.2

    Turning Points

    The section explores critical points, turning points, and their significance in identifying local maxima and minima of functions using derivatives.

    Learning Practice

  • 2

    Using The First Derivative

    The first derivative is used to identify critical points of a function, which help in determining local maxima and minima.

    Learning Practice

  • 2.1

    First Derivative Test

    The First Derivative Test helps identify local maximum and minimum points of functions by examining critical points where the derivative is zero or undefined.

    Learning Practice

  • 3

    Using The Second Derivative

    The second derivative test is a crucial tool for determining the nature of critical points in a function.

    Learning Practice

  • 3.1

    Second Derivative Test

    The Second Derivative Test is a method used to classify critical points of a function to determine whether they are local maxima, local minima, or points of inflection.

    Learning Practice

  • 4

    Step-By-Step Method For Finding Maxima/minima

    This section outlines a systematic method for identifying maxima and minima of functions using derivatives.

    Learning Practice

  • 5

    Examples

    This section presents practical examples illustrating how to find maxima and minima using derivatives.

    Learning Practice

  • 5.1

    Example 1

    The section covers the concepts of maxima and minima in calculus, explaining how to identify critical points and classify them using first and second derivatives.

    Learning Practice

  • 5.2

    Example 2

    This section introduces optimization problems using calculus, focusing on finding local maxima and minima through the application of first and second derivative tests.

    Learning Practice

  • 6

    Application: Optimization Problem

    This section explores how to find the maximum area of a rectangle given a fixed perimeter using calculus techniques.

    Learning Practice

  • 7

    Summary

    This section explains how to identify maximum and minimum values of functions using calculus, particularly derivatives.

    Learning Practice

  • 8

    Key Takeaways

    This section highlights essential points related to finding maximum and minimum values of functions using derivatives.

    Learning Practice

References

10 IB calculus ch5.pdf

Class Notes

Memorization

Revision Tests