MATH 124 Calculus & Analytic Geometry I

Covers derivatives, computing derivatives, curve sketching, optionalization, and problem solving. Prerequisite: C or better in MATH 105 or placement test (NS, QS)

Credits

5

Outcomes

1. Define, calculate (or estimate) and give a geometric interpretation of the limit of a function at a point.
2. Define continuity and differentiability, and give examples of functions that are discontinuous and/or not differentiable.
3. Interpret the derivative of a function at a point BOTH as the instantaneous rate of change in the quantity modeled AND as the slope of the tangent line to the graph.
4. Sketch the graph of the derivative and the antiderivative from the graph of a given function.
5. Compute (or estimate) the value of the derivative at a point using the limit definition.
6. Compute the expression for the derivative of some elementary functions from the limit definition, and using “rules” of differentiation (including the power rule, product rule, quotient rule and chain rule).
7. Interpret the value of the first and second derivative as measures of increase and concavity of functions.
8. Apply basic optimization techniques to selected problems arising in various fields such as physical modeling, economics and population dynamics.