### Understanding Critical Numbers and ExtremaThe provided graph depicts a function over the interval \([-5, 5]\).#### Approximate the critical numbersThe critical numbers are the x-values at which the derivative of the function equals zero or does not exist. These are points where the function's slope changes signs and often correspond to local maxima, minima, or points of inflection.Place your approximation in the following box:\[ x = \_\_\_\_\_\_\_\_\_\_\_\_ \]#### Identify the ExtremaNext, determine whether these critical numbers correspond to relative maxima, relative minima, absolute maxima, or absolute minima by comparing the function's values.##### Points of Interest in the Graph:- **Relative Maxima**: These are points where the function reaches a local high within a neighborhood around the point.- **Relative Minima**: These are points where the function reaches a local low within a neighborhood around the point.- **Absolute Maxima**: This is the highest point over the entire interval.- **Absolute Minima**: This is the lowest point over the entire interval.Fill in the critical numbers at which each phenomenon occurs:- **Relative Maxima** \( x = \_\_\_\_\_\_\_ \)- **Relative Minima** \( x = \_\_\_\_\_\_\_ \)- **Absolute Maxima** \( x = \_\_\_\_\_\_\_ \)- **Absolute Minima** \( x = \_\_\_\_\_\_\_ \)If an answer does not exist, please enter "DNE" (Does Not Exist).#### Detailed Explanation of the Graph:The parabola, which appears to open downwards, suggests:- A peak (maximum point) at approximately \( x = 1 \) where \( y \approx 4 \), suggesting a potential relative (and possibly absolute) maximum.- Points where the function intercepts the x-axis (roots) provide insights into where the function changes from increasing to decreasing.Using these insights, fill in the necessary fields to complete the analysis. This task emphasizes your understanding of critical numbers and how to interpret them in the context of the graph.

Name: ### Understanding Critical Numbers and ExtremaThe provided graph depi
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: ### Understanding Critical Numbers and ExtremaThe provided graph depicts a function over the interval \([-5, 5]\).#### Approximate the critical numbersThe critical numbers are the x-values at which the derivative of the function equals zero or does