Algebra

C.A.10State and apply the formal definition of a derivative.C.A.11Apply differentiation rules to sums, products, quotients, and powers of functions.C.A.12Use the chain rule and implicit differentiation.C.A.13Describe the relationship between differentiability and continuity.C.A.15Define a derivative and explain the purpose/utility of the derivative.C.A.16Apply the derivative as a rate of change in varied contexts, including velocity, speed, and acceleration.C.A.17Apply the derivative to find tangent lines and normal lines to given curves at given points.C.A.18Predict and explain the relationships between functions and their derivatives.C.A.19Model rates of change to solve related rate problems.C.A.20Solve optimization problems.C.A.21State and apply the First and Second Fundamental Theorem of Calculus.C.A.22Apply the power rule and u-substitution to evaluate indefinite integrals.C.A.4Predict and explain the characteristics and behavior of functions and their graphs (domain, range, increasing/decreasing intervals, intercepts, symmetry, and end behavior).C.A.5Investigate, describe, and determine asymptotic behavior using tables, graphs, and analytical methodsC.A.6Determine and justify the continuity and discontinuity of functionsC.A.7Solve mathematical situations and application problems involving or using derivatives, including exponential, logarithmic, and trigonometric functions.C.A.8Calculate limits using algebraic methods.C.A.9Verify the behavior and direction of non-determinable limits.
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