Identify and explain situations in which slope is used to describe a rate of change.

Interpret and explain the difference between average rate of change and instantaneous rate of change.

Solve situational problems involving average rates of change and instantaneous rates of change.

Develop, explain, and apply strategies for determining the slope of the tangent line at a particular point by finding the slopes of secant lines.

Develop, explain, and apply the following definition of a derivative: $\lim_{h→0}{f(x+h)-f(x)}/h$

Develop, explain, and apply rules of differentiation:

• power
• product
• quotient
• chain.

Apply two or more differentiation rules to a function.

Critique the statement, “It is possible to differentiate any function with the rules that we have studied.”

Identify the value(s) of x where a function is not differentiable.

Critique the statement, “If a function is continuous, then it is differentiable.”

Develop, explain, and apply the process of implicit differentiation.

Determine the equation of the tangent line and normal line at a specific point on a function.

Express derivatives using a variety of notations such as $f'(x)$, $y'$, $d/d_\x$, and $d_\y/d_\x$.

Critique the statement, “The $f'(x)$ notation for the derivative is superior to the $d_\y/d_\x$ notation.”