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RELATED RATES CUBES SQUARES (IMPLICIT DIFFERENTIATION)VIDEO TUTORIALSRELATED LINKS
APPLICATION OF DERIVATIVES VIDEOS
1. Extreme Value Theorem Graphical 2. Extreme Value Theorem Algebraic and Graphical 3. Connecting f' and f" with the graph of f pt I 4 . Connecting f' and f" with the graph of f pt II 5. Mean Value Theorem Pt I 6. Mean Value Theorem Pt II 7. Optimization and Modelling Part I Rectangular Box Square Cut 8. Optimization and Modelling Part II Enclosed Cylindrical Can 9. Optimizaiton and Modelling Part III Cylinder Inscribed in a cone 10. Related Rates Formulas Practice 11. Related Rates Squares Cubes |
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AP Calculus Standards Covered in this Section
The student will define and apply the properties of limits of functions. Limits will be
evaluated graphically and algebraically. This will include
a) limits of a constant;
b) limits of a sum, product, and quotient;
c) one-sided limits; and
d) limits at infinity, infinite limits, and non-existent limits. *
*AP Calculus BC will include l’Hopital’s Rule, which will be used to find the limit of
functions whose limits yield the indeterminate forms: 0/0 and ∞/∞.
APC.3 The student will use limits to define continuity and determine where a function is
continuous or discontinuous. This will include
a) continuity in terms of limits;
b) continuity at a point and over a closed interval;
c) application of the Intermediate Value Theorem and the Extreme Value Theorem; and
d) geometric understanding and interpretation of continuity and discontinuity.
APC.4 The student will investigate asymptotic and unbounded behavior in functions. This will
include
a) describing and understanding asymptotes in terms of graphical behavior and limits
involving infinity; and
b) comparing relative magnitudes of functions and their rates of change.
The student will define and apply the properties of limits of functions. Limits will be
evaluated graphically and algebraically. This will include
a) limits of a constant;
b) limits of a sum, product, and quotient;
c) one-sided limits; and
d) limits at infinity, infinite limits, and non-existent limits. *
*AP Calculus BC will include l’Hopital’s Rule, which will be used to find the limit of
functions whose limits yield the indeterminate forms: 0/0 and ∞/∞.
APC.3 The student will use limits to define continuity and determine where a function is
continuous or discontinuous. This will include
a) continuity in terms of limits;
b) continuity at a point and over a closed interval;
c) application of the Intermediate Value Theorem and the Extreme Value Theorem; and
d) geometric understanding and interpretation of continuity and discontinuity.
APC.4 The student will investigate asymptotic and unbounded behavior in functions. This will
include
a) describing and understanding asymptotes in terms of graphical behavior and limits
involving infinity; and
b) comparing relative magnitudes of functions and their rates of change.