C.D.CD.A.4 Demonstrate the relationship between differentiability and continuity.
C.D.CD.B Understand the derivative at a point.
C.D.CD.B.5 Interpret the derivative as the slope of a curve (which could be a line) at a point, including points at which there are vertical tangents and points at which there are no tangents (i.e., where a function is not locally linear).
C.D.CD.B.9 Understand Rolle's Theorem as a special case of the Mean Value Theorem.
C.D.AD Computing and Applying Derivatives
C.D.AD.A Apply differentiation techniques.
C.D.AD.A.1 Describe in detail how the basic derivative rules are used to differentiate a function; discuss the difference between using the limit definition of the derivative and using the derivative rules.
C.D.AD.A.2 Calculate the derivative of basic functions (power, exponential, logarithmic, and trigonometric).
C.D.AD.C.18 Use tangent lines to approximate function values and changes in function values when inputs change (linearization).
C.I.UI Understanding Integrals
C.I.UI.A Demonstrate understanding of a definite integral.
C.I.UI.A.1 Define the definite integral as the limit of Riemann sums and as the net accumulation of change.
C.I.UI.A.2 Correctly write a Riemann sum that represents the definition of a definite integral.
C.I.UI.A.3 Use Riemann sums (left, right, and midpoint evaluation points) and trapezoid sums to approximate definite integrals of functions represented graphically, numerically, and by tables of values.
C.I.UI.B Understand and apply the Fundamental Theorem of Calculus.
C.I.UI.B.4 Recognize differentiation and antidifferentiation as inverse operations.
C.I.UI.B.5 Evaluate definite integrals using the Fundamental Theorem of Calculus.
C.I.UI.B.6 Use the Fundamental Theorem of Calculus to represent a particular antiderivative of a function and to understand when the antiderivative so represented is continuous and differentiable.