Search the California Content Standards

Standard:
Students demonstrate an understanding of the derivative of a function as the slope of the tangent line to the graph of the function.

Standard:
Students demonstrate an understanding of the interpretation of the derivative as an instantaneous rate of change. Students can use derivatives to solve a variety of problems from physics, chemistry, economics, and so forth that involve the rate of change of a function.

Standard:
Students understand the relation between differentiability and continuity.

Standard:
Students derive derivative formulas and use them to find the derivatives of algebraic, trigonometric, inversetrigonometric, exponential, and logarithmic functions.

Standard:
Students know the chain rule and its proof and applications to the calculation of the derivative of a variety of composite functions.

Standard:
Students find the derivatives of parametrically defined functions and use implicit differentiation in a wide variety of problems in physics, chemistry, economics, and so forth.

Standard:
Students compute derivatives of higher orders.

Standard:
Students know and can apply Rolle’s Theorem, the mean value theorem, and L’Hôpital’s rule.

Standard:
Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.

Cluster:
Build a function that models a relationship between two quantities. [Include all types of functions studied.]

Standard:
Write a function that describes a relationship between two quantities. * Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. *