Studio di funzione con radice quadrata- Compito d'esame Analisi matematica 1

Study of a function with a square root, taken from an assignment given in a written exam in mathematical analysis 1. This video addresses the study of an irrational function containing an absolute value step by step. The even function will significantly simplify the solution, saving a considerable amount of calculations. The fundamental steps for studying a function are: Determining the domain or set of definition. Finding any asymptotes using the calculus of limits. Monotonicity and finding any relative or absolute maximums and/or minimums using the first derivative, as well as studying differentiability to identify any corner points, cusp points, or inflection points with a vertical tangent. We will note that, although the function is continuous across the entire set of real numbers, it will have a point of non-differentiability of the cusp type. The study of the second derivative was intentionally omitted (clearly specified in the assignment requirements) because it would have involved several significant algebraic steps (given the structure of the first derivative) and would not have provided vital information for plotting the graph. In the end, a qualitative graph was drawn in the Cartesian diagram. Further studies of interesting functions (for both university and high school students) can be found at the following links:    • Studio di funzione con logaritmo e valore ...   (study of a function with a logarithm and absolute value)    • Studio di funzione .Esercizio d'esame semp...   (simple study of a function for beginners) #salvoromeo #analisimatematica1 #studiodifunzione