Math Problem Statement

The exercise asks to analyze the function f(x) = x / sqrt(x^2 - 2), including finding its existence set, monotonicity intervals, limits at extreme points, graph depiction, max/min points, and concavity/convexity intervals.

Solution

The image contains an exercise for a final exam on "Mathematics for Economics" with the following tasks related to the given function f(x)=xx2−2f(x) = \frac{x}{\sqrt{x^2 - 2}}:

  1. Compute the existence set of ff.
  2. Find the intervals of monotonicity for the function ff.
  3. Compute the limits of ff at the extreme points of the existence set.
  4. Depict the graph of ff and find the local and global max/min points of ff in the existence set.
  5. Find the intervals of concavity/convexity for the function ff.

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Math Problem Analysis

Mathematical Concepts

Calculus
Differentiation
Limits
Function Analysis
Concavity and Convexity
Monotonicity
Existence Set

Formulas

f(x) = x / sqrt(x^2 - 2)
Derivative for monotonicity
Limit properties
Concavity/Convexity tests

Theorems

Intermediate Value Theorem
First Derivative Test
Second Derivative Test
Existence and Continuity of Functions

Suitable Grade Level

College/University (Mathematics for Economics)

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