Learning Objective 2.1A

Learning Objective 2.1A Students will be able to identify the derivative of a function as the limit of a difference quotient.

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Before you can learn the shortcuts of differentiation, you should learn the theory and the foundational method. We'll start with that here and learn some basic notation

Essential Knowledge 2.1A.1 Shows you how to use difference quotients to find average rates of change

Essential Knowledge 2.1A.2 Shows you how to combine limits with difference quotients to find instantaneos rates of change

Essential Knowledge 2.1A.3 Shows you that the limit of the difference quotient is called a derivative.

Essential Knowledge 2.1A.4 Shows you different symbols for derivatives

Essential Knowledge 2.1A.5 Shows you how to represent derivatives graphically, numerically, analytically, and verbally.

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Essential Knowledge 2.1A1 Students will know that the difference quotients

and express the average rate of change of a function over an interval.

Essential Knowledge 2.1A2 Students will know that the instantaneous rate of change of a function at a point can be expressed by

or , provided that the limit exists. These are common forms of the definition of the derivative and are denoted f '(a).

Essential Knowledge 2.1A3 Students will know that the derivative of f is the function whose value at x is provided this limit exists.

Essential Knowledge 2.1A4 Students will know that for y = f(x), notations for the derivative include , f '(x), and y'.

Essential Knowledge 2.1A5 Students will know that the derivative can be represented graphically, numerically, analytically, and verbally.