Question

Найти экстремум функций

Answer 1

Ответ:

Вот пример)

Пошаговое объяснение:

надеюсь понятно

Answer 2

Finding Extrema of Functions

To find the extrema of a function, we can use the first and second derivative tests. The first derivative test helps us identify critical points, and the second derivative test helps us determine whether these critical points correspond to a local minimum, local maximum, or neither.

First Derivative Test: The first derivative test helps us identify critical points where the function's derivative is zero or undefined. These critical points can correspond to local extrema.

Second Derivative Test: The second derivative test involves analyzing the concavity of the function at the critical points identified using the first derivative test. If the second derivative is positive at a critical point, the function has a local minimum at that point. If the second derivative is negative, the function has a local maximum at that point. If the second derivative is zero, the test is inconclusive.

Let's apply these tests to the given functions to find their extrema.

Function 1: The first function involves a sequence of operations and relationships between variables X and Y. The provided snippet doesn't explicitly define a function, so it's challenging to apply the first and second derivative tests without the specific function.

Function 2: The second function involves mathematical operations with variables X and Y. However, it doesn't provide a clear definition of a function, making it difficult to apply the first and second derivative tests.

Function 3: The third function snippet doesn't provide a clear definition of a function, making it challenging to apply the first and second derivative tests.

Function 4: The fourth function snippet also lacks a clear definition of a function, making it difficult to apply the first and second derivative tests.

Function 5: The fifth function snippet mentions a sequence of operations and relationships involving variable k. However, it doesn't explicitly define a function, making it challenging to apply the first and second derivative tests.

Function 6: The sixth function snippet doesn't provide a clear definition of a function, making it difficult to apply the first and second derivative tests.

Function 7: The seventh snippet doesn't provide a mathematical function, so it's not possible to apply the first and second derivative tests.

Function 8: The eighth snippet doesn't contain a mathematical function, so the application of the first and second derivative tests is not feasible.

Function 9: The ninth snippet doesn't provide a mathematical function, making it challenging to apply the first and second derivative tests.

Function 10: The tenth snippet presents two functions, z=3x^2+xy+2y^2+4x-7y+15 and z=-x^2+2xy. These functions can be analyzed using the first and second derivative tests to find their extrema.

Given the limitations of the provided snippets, it's essential to have the complete mathematical functions to effectively apply the first and second derivative tests for finding extrema. If you have the complete functions, please provide them for further analysis.