Real-valued functions of a real variable; into, onto and one-to-one functions; sum, difference, product and quotient of two functions; composite functions; absolute value, polynomial, rational, trigonometric, exponential and logarithmic functions
Limit and continuity of a function; limit and continuity of the sum, difference, product and quotient of two functions; L'Hôpital rule of evaluation of limits; continuity of composite functions; intermediate value property of continuous functions
Derivative of a function; derivative of the sum, difference, product and quotient of two functions; chain rule; derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions
Derivatives of implicit functions; derivatives up to order two; geometrical interpretation of the derivative; tangents and normals; increasing and decreasing functions; maximum and minimum values of a function
Rolle's theorem and Lagrange's mean value theorem and their geometric interpretation