# 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

- Define, calculate (or estimate) and give a geometric interpretation of the limit of a function at a point.
- Define continuity and differentiability, and give examples of functions that are discontinuous and/or not differentiable.
- 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.
- Sketch the graph of the derivative and the antiderivative from the graph of a given function.
- Compute (or estimate) the value of the derivative at a point using the limit definition.
- 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).
- Interpret the value of the first and second derivative as measures of increase and concavity of functions.
- Apply basic optimization techniques to selected problems arising in various fields such as physical modeling, economics and population dynamics.