### Analyzing Polynomial Functions#### Problem Statement:Let $ y = f(x) = 3x^3 - 6.2x^2 + 2.8x - 4.3 $. Use a graphing calculator and an appropriate window to analyze the function.---#### Tasks:**a) Sketch the graph of $ f $ and label all relative extrema:**- You are asked to plot the graph of the function provided. The graph should include all relative maxima and minima, clearly labeled. Use graphing tools to identify these points accurately.The provided image of the graph is a simple coordinate axis layout:- The horizontal axis is labeled as $ x $, extending from approximately $-1.5$ to $3.2$.- The vertical axis is labeled as $ y $, extending from $-8$ to $2$.**b) Determine the coordinates of all relative maxima and minima:**To find these coordinates, utilize the "max/min" features on your graphing calculator. The relative extrema are critical points where the function changes from increasing to decreasing or vice versa.- **Relative Maxima**: The peaks on the graph where the function changes from increasing to decreasing.- **Relative Minima**: The valleys on the graph where the function changes from decreasing to increasing.**c) Identify intervals where $ f $ is increasing or decreasing:**Analyze the graph to see where the function's slope is positive (increasing function) or negative (decreasing function).- **Increasing on**: List the intervals of $ x $ where the graph ascends.- **Decreasing on**: List the intervals of $ x $ where the graph descends.**d) Find all critical values of $ x $:**Critical values occur where the derivative of $ f(x) $ is zero or undefined. These points are essential for determining relative maxima and minima. Use calculus techniques or graphing tools to find these values.Use this analysis to understand how the function behaves, the location of its critical points, and the nature of its graph, which will provide insights into the function's overall trajectory.

Name: ### Analyzing Polynomial Functions#### Problem Statement:Let $ y = f
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Description: ### Analyzing Polynomial Functions#### Problem Statement:Let \( y = f(x) = 3x^3 - 6.2x^2 + 2.8x - 4.3 $. Use a graphing calculator and an appropriate window to analyze the function.---#### Tasks:**a) Sketch the graph of $ f $ and label all relati

Given that f(x)=3x3-6.2x2+2.8x-4.3 To find the critical points Find the derivative of f(x)…

Answered: let y= fix)= 3x3–6.2x* +2.8x-4.3 (Use…

Math

Calculus

let y= fix)= 3x3–6.2x* +2.8x-4.3 (Use grapning Calculator and appropriate wndaw

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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Question

### Analyzing Polynomial Functions

#### Problem Statement:
Let $ y = f(x) = 3x^3 - 6.2x^2 + 2.8x - 4.3 $. Use a graphing calculator and an appropriate window to analyze the function.

---

#### Tasks:

**a) Sketch the graph of $ f $ and label all relative extrema:**

- You are asked to plot the graph of the function provided. The graph should include all relative maxima and minima, clearly labeled. Use graphing tools to identify these points accurately.

The provided image of the graph is a simple coordinate axis layout:
- The horizontal axis is labeled as $ x $, extending from approximately $-1.5$ to $3.2$.
- The vertical axis is labeled as $ y $, extending from $-8$ to $2$.

**b) Determine the coordinates of all relative maxima and minima:**

To find these coordinates, utilize the "max/min" features on your graphing calculator. The relative extrema are critical points where the function changes from increasing to decreasing or vice versa.

- **Relative Maxima**: The peaks on the graph where the function changes from increasing to decreasing.
- **Relative Minima**: The valleys on the graph where the function changes from decreasing to increasing.

**c) Identify intervals where $ f $ is increasing or decreasing:**

Analyze the graph to see where the function's slope is positive (increasing function) or negative (decreasing function).

- **Increasing on**: List the intervals of $ x $ where the graph ascends.
- **Decreasing on**: List the intervals of $ x $ where the graph descends.

**d) Find all critical values of $ x $:**

Critical values occur where the derivative of $ f(x) $ is zero or undefined. These points are essential for determining relative maxima and minima. Use calculus techniques or graphing tools to find these values.

Use this analysis to understand how the function behaves, the location of its critical points, and the nature of its graph, which will provide insights into the function's overall trajectory.

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