Please respond D, G and H. **Title: Understanding Graph Sketching for the Function \( y = 4x^3 - 6x^2 - 24x \)**In this lesson, we will explore how to sketch the graph of the polynomial function given by \( y = 4x^3 - 6x^2 - 24x \) by following a structured set of guidelines:a. **Asymptotic Behavior**: Analyze how the function behaves as \( x \) approaches very large positive or negative values.b. **First Derivative**: Compute the first derivative to find the rate of change of the function, which helps in identifying the slope of the tangent line to the curve at any point.c. **Increasing and Decreasing Intervals**: Use the first derivative to determine where the function is increasing or decreasing.d. **Critical Points and Extrema**: Locate critical points by setting the first derivative to zero and solve for \( x \). Determine which of these are local maxima or minima.e. **Second Derivative**: Calculate the second derivative to understand the concavity of the function.f. **Inflection Points**: Identify points where the concavity changes using the second derivative.g. **Concavity**: Determine intervals over which the function is concave upward or concave downward by analyzing the sign of the second derivative.h. **Curve Sketching**: Combine all the information above to draw a rough sketch of the function's graph, illustrating key features like critical and inflection points, and behavior at extreme values of \( x \).This systematic approach allows for a comprehensive understanding of the function's graphical behavior.

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Sketch a graph of the following function by the guidelines: y = 4x3 – 6x? – - a. The behavior of y when x becomes very large positive or very large negative. b. The first derivative c. The increasing intervals and decreasing intervals d. The critical points and max points or min points e. The second derivative f. The reflection points g. The concave upward intervals and concave downward intervals h. Draw the curve sketching

Sketch a graph of the following function by the guidelines: y = 4x3 – 6x? – - a. The behavior of y when x becomes very large positive or very large negative. b. The first derivative c. The increasing intervals and decreasing intervals d. The critical points and max points or min points e. The second derivative f. The reflection points g. The concave upward intervals and concave downward intervals h. Draw the curve sketching

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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