This course is an introduction to differential calculus. Students explore limits and continuity. They examine the basic concept of differentiation and practice differentiation techniques. Students develop competence applying differentiation to solve problems. Students also examine simple antiderivatives.
Recover the antiderivative of simple polynomial and trigonometric functions.
Approximate a solution to an equation using Newton’s method.
Solve applied optimization problems.
Graphing and Applications
Determine critical points and points of inflection of functions with derivatives.
Find local extrema using the first derivative of a monotonic function.
Use the Mean Value Theorem to find the derivative of a continuous function.
Use derivatives to find extreme values of functions.
Chain Rule and Related Rates
Approximate derivatives using linearization.
Derive rates of change from related known rates of change.
Calculate the derivative of multivariable expressions, implicit differentiation.
Find the derivative of the composition of two functions.
Compute the derivative of trigonometric functions.
Recognize derivatives as rates of change.
Find the derivative of the ratio and the product of two functions.
Find the derivative of the sum and difference of two functions.
Compute the derivatives of linear, quadratic, and polynomial functions.
Limits and Continuity
Identify asymptotes of graphs.
Determine the continuity of functions at given points.
Calculate one-sided limits.
Calculate limits of functions.
Functions and Rates of Change
Use limit laws to find limits of functions.
Calculate slopes of tangent lines at given points.
Graph trigonometric functions.
Determine the effects of operations on a graph.
Recognize mathematical functions from graphs.
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