Applications of Differentiation I-Related Rates and Extrema
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Problem Solving Drill |
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| "Title" Tutorial Summary : |
This tutorial describes application of differentiation such as related rated and extrema. By completing this tutorial you will create and analyze graphs of functions and their first derivatives. Also, examples showing the relative and absolute maxima and minima for a function are introduced with the help of examples.
Next, learning how to take derivatives implicitly is shown with the aid of example problems. Related rates problems are given with the introduction of example problems. The use of the KUDOS problem solving method is introduced to emphasize the concept of related rates and their applications. Graphs of the derivatives of functions are shown to point out the maximum and minimum values of a typical function.
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| Tutorial Features: |
Specific Tutorial Features:
- Graphic representation of derivatives.
- Example problems showing related rates problems.
- Implicit differentiation is shown with the use of derivatives and tangent lines.
Series Features:
- Concept map showing inter-connections of new concepts in this tutorial and those previously introduced.
- Definition slides introduce terms as they are needed.
- Visual representation of concepts
- Animated examples—worked out step by step
- A concise summary is given at the conclusion of the tutorial.
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| "Title" Topic List: |
Graphs of functions and their derivatives
Going to (and Finding) Extremes
Related maximum and minimum defined
The definition of a critical number
Finding extremes
Implicit differentiation
Definition of implicit differentiation
Related rate problems
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is the minimum of 
on an interval if 
for all 
on that interval.
is the maximum of 
on an interval if 
for all 
on that interval.
is the minimum of 
on an interval if 
for all x on that interval, then it sis a relative minimum.
is the maximum of 
on an interval if 
for all x on that interval, then it is a relative maximum.
be defined at a point, 
If 
or if 
is not differentiable at 
then 
is a critical number of 
then over the interval 
there must exist at least one maximum and one minimum.
