Unit II
The Derivative
(22 days 1 test)
1.
The Derivative of a Function
Definition of the Derivative as a limit of the difference quotient
Alternate Definition of the Derivative at a Point
Recognizing a given limit as a derivative
Expressing the derivative as a limit
OneSided Derivatives Can Differ at a Point
2.
Differentiability
(APPENDIX A)
The Difference Quotient and the Symmetric Difference Quotient
Computing a Numerical Derivative (algebraically and numerically)
Using the Symmetric Difference Quotient to estimate the derivative at a point
Sketching a Graph of
f
from the Derivative
Differentiability Implies Continuity (yet continuity does not imply
differentiability)
3.
Rules for Differentiation
Basic Rules (Derivative of a Constant, Power Rule, Constant Multiple Rule, Sum
and Difference Rule)
Finding Horizontal Tangents
Working With Numerical Values
Second and Higher Order Derivatives
4.
Velocity and Other Rates of Change
Slope of a secant line / Slope of a tangent line
Average velocity / Instantaneous velocity
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 Spring '10
 John
 Calculus, Derivative, flu, 22 days

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