Kinda stuck, pls help. Thanks **Title: Analyzing Critical Points, Discontinuities, and Intervals of Increase and Decrease****Example Problem**:**Function:**\[ y = -x^3 + 2x^2 + 2 \]**Instructions:**For each problem, find the x-coordinates of all critical points, find all discontinuities, and find the open intervals where the function is increasing and decreasing.**Graph Analysis:**Below the instructions, there is a graph illustrating the function $ y = -x^3 + 2x^2 + 2 $. The graph provides a visual representation of the function’s behavior. ### Graph Details:- **X-axis**: Represents the range for the variable $ x $.- **Y-axis**: Represents the range for the function values $ y $. - The curve starts from the upper left, descending into a local minimum, then rises to a local maximum, and finally descends again towards the lower right of the graph.- The grid is divided at unit intervals for both axes, aiding in identifying critical points and intervals of increase and decrease.### Analytical Steps:1. **Finding Critical Points:** - To find the x-coordinates of all critical points, solve $ \frac{dy}{dx} = 0 $. - Use the first derivative test or analyze the graph to locate local maxima and minima.2. **Identifying Discontinuities:** - Look for any breaks, asymptotes, or undefined points within the given function.3. **Determining Intervals of Increase and Decrease:** - Use the first derivative test or visually interpret the graph to find where the function is increasing (rising left to right) and decreasing (falling left to right).Applying these steps will facilitate a clear understanding of the function and its behavior over the domain.

For critical points, do dy/dx= 0 and critical points.

Answered: For each problem, find the…

For each problem, find the x-coordinates of all critical points, find all discontinuities, and find the o intervals where the function is increasing and decreasing. y=-x' + 2x + 2

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Estimation

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Kinda stuck, pls help. Thanks

**Title: Analyzing Critical Points, Discontinuities, and Intervals of Increase and Decrease**

**Example Problem**:

**Function:**
\[ y = -x^3 + 2x^2 + 2 \]

**Instructions:**
For each problem, find the x-coordinates of all critical points, find all discontinuities, and find the open intervals where the function is increasing and decreasing.

**Graph Analysis:**

Below the instructions, there is a graph illustrating the function $ y = -x^3 + 2x^2 + 2 $. The graph provides a visual representation of the function’s behavior.

### Graph Details:
- **X-axis**: Represents the range for the variable $ x $.
- **Y-axis**: Represents the range for the function values $ y $.
- The curve starts from the upper left, descending into a local minimum, then rises to a local maximum, and finally descends again towards the lower right of the graph.
- The grid is divided at unit intervals for both axes, aiding in identifying critical points and intervals of increase and decrease.

### Analytical Steps:

1. **Finding Critical Points:**
- To find the x-coordinates of all critical points, solve $ \frac{dy}{dx} = 0 $.
- Use the first derivative test or analyze the graph to locate local maxima and minima.

2. **Identifying Discontinuities:**
- Look for any breaks, asymptotes, or undefined points within the given function.

3. **Determining Intervals of Increase and Decrease:**
- Use the first derivative test or visually interpret the graph to find where the function is increasing (rising left to right) and decreasing (falling left to right).

Applying these steps will facilitate a clear understanding of the function and its behavior over the domain.

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