The lessons will be given individually in English and can take place face to face or online.
All essential points of the study of function covered in the Mathematics A program for Years 10th, 11th and 12th of secondary education in Portugal will be covered. In particular, the following topics will be addressed:
Definition of function.
Domain and Range of the function.
Operations with functions.
Inverse function and composition of functions.
Monotony increasing and decreasing functions.
Function extremes.
Period of the function.
Function types (linear, polynomial, absolute value, exponential, logarithm, nth root and rational).
Function transformations.
Inequalities with functions.
Function limit, Calculation of limits and Indeterminate Forms. Remarkable limits.
Derivative of a Function. Techniques of Differentiation.
Continuity of the function. Mean value, intermediate value and extreme value theorems.
Concavity, inflection points and second derivative.
Trigonometry and trigonometric functions. Trigonometric formulas.
Law of sines and cosines.
Trigonometric equations.
Derivative of trigonometric functions.
In our “resources” section you can find a list of useful links to help the student in this approach to calculus.