mth280 | undergraduate
topic title goes here
Functions and Rates of Change
- Calculate slopes of tangent lines at given points.
- Use limit laws to find limits of functions.
- Recognize mathematical functions from graphs.
- Determine the effects of operations on a graph.
- Graph trigonometric functions.
Limits and Continuity
- Calculate one-sided limits.
- Calculate limits of functions.
- Determine the continuity of functions at given points.
- Identify asymptotes of graphs.
Graphing and Applications
- Use derivatives to find extreme values of functions.
- Find local extrema using the first derivative of a monotonic function.
- Use the Mean Value Theorem to find the derivative of a continuous function.
- Determine critical points and points of inflection of functions with derivatives.
- Compute the derivative of trigonometric functions.
- Compute the derivatives of linear, quadratic, and polynomial functions.
- Find the derivative of the sum and difference of two functions.
- Find the derivative of the ratio and the product of two functions.
- Recognize derivatives as rates of change.
Chain Rule and Related Rates
- Find the derivative of the composition of two functions.
- Calculate the derivative of multivariable expressions, implicit differentiation.
- Derive rates of change from related known rates of change.
- Approximate derivatives using linearization.
More Applications of Derivatives
- Solve applied optimization problems.
- Approximate a solution to an equation using Newton’s method.
- Recover the antiderivative of simple polynomial and trigonometric functions.
Calculus I Concept Review
- Apply the concepts presented in this course.
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