LC.1.C Students will determine the limit of a function at a value numerically, graphically, and analytically
LC.1.C.1 Identify vertical asymptotes in rational and logarithmic functions by identifying locations where the function value approaches infinity; estimate limits numerically and graphically; calculate limits analytically: algebraic simplification, direct substitution, one-sided limits, rationalization.
LC.1.C.5 Identify and classify graphically, algebraically, and numerically if a discontinuity is removable or non-removable; identify the three conditions that must exist in order for a function to be continuous at x = a: f(a) is defined, the limit as x approaches a of f(x) equals f(a), the limit as x approaches a of f(x) exists.
D.2.C.3 Establish and apply the relationship between differentiability and continuity.
D.2.C.4 Compare the characteristic of graphs of ƒ and f': generate the graph of f given the graph of f' and vice versa, establish the relationship between the increasing and decreasing behavior of ƒ and the sign of f', identify maxima and minima as points where increasing and decreasing behavior change.
D.2.C.5 Apply the Mean Value Theorem on a given interval.
D.2.C.6 Compare the characteristic of graphs of ƒ, f', and f": generate the graphs of f and f' given the graph of f" and vice versa, establish the relationship between the concavity of ƒ and the sign of f", identify points of inflection as points where concavity changes.
D.2.C.7 Find derivatives of functions using: power rule, product rule, quotient rule.
D.2.C.8 Find derivatives of: an implicitly defined equation, composite functions using chain rule, exponential and logarithmic functions, functions requiring the use of more than one differentiation rule.