Question

Постройте график функции y=2x^3+3x^2-8x-12/(2x+3) (x+2 ) и определите, при каком значении параметра n прямая y=n НЕ имеет с графиком общих точек.

Answer 1

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Answer 2

Function and Graph Analysis

To analyze the function \( y = \frac{2x^3 + 3x^2 - 8x - 12}{2x + 3} + (x + 2) \) and determine the value of the parameter \( n \) for which the line \( y = n \) does not intersect the graph, we can follow these steps:

1. Identify the Critical Points: Find the critical points of the function to understand its behavior. 2. Graph the Function: Plot the graph of the function to visualize its shape and behavior. 3. Analyze the Line: Determine the conditions for the line \( y = n \) to not intersect the graph.

Let's proceed with these steps to analyze the function and determine the value of \( n \) for which the line \( y = n \) does not intersect the graph.

1. Identify the Critical Points

The critical points of the function can be found by setting the derivative equal to zero and solving for \( x \).

2. Graph the Function

Plot the graph of the function \( y = \frac{2x^3 + 3x^2 - 8x - 12}{2x + 3} + (x + 2) \) to visualize its behavior.

3. Analyze the Line

Determine the conditions for the line \( y = n \) to not intersect the graph.

Let's proceed with the calculations and graphing to determine the value of \( n \) for which the line \( y = n \) does not intersect the graph.