2a. 2b. **Title: Analyzing Critical Points and Local Minima from a Derivative Graph****Content:**2) Suppose \( g \) is a continuous function on the interval \((-5, 4)\). The graph of \( g' \), the derivative of \( g \), is given in the figure below.**Graph Analysis:**The graph displays the derivative \( g' \) of the function \( g \) over the interval \((-5, 4)\). The graph can be described as follows:- From \( x = -5 \) to \( x = -3 \), the graph rises, crossing the x-axis at \( x = -4 \). - From \( x = -3 \) to \( x = 1 \), the graph decreases, crossing the x-axis at \( x = -1 \).- From \( x = 1 \) to \( x = 4 \), the graph increases again, crossing the x-axis at \( x = 3 \).Noticeable points on the graph include:- Peaks or valleys where the curve changes direction (possible critical points).- Intervals where the derivative \( g' \) is positive (function \( g \) increases).- Intervals where the derivative \( g' \) is negative (function \( g \) decreases).**Exercises:**a) **List all the critical points (if any) of \( g \) in the interval \((-5, 4)\). Write "NONE" if appropriate.** \[ x = \_\_\_\_\_\_\_\_\_\_\_\_ \]b) **At what point (or points) does the function \( g \) have a local minimum? Write "NONE" if appropriate.** \[ x = \_\_\_\_\_\_\_\_\_\_\_\_ \]**Guidance for Answering:**- **Critical Points:** Critical points occur where the derivative \( g' \) is zero or undefined. Observe where the graph crosses the x-axis.- **Local Minima:** A local minimum can occur at a critical point where \( g' \) changes from negative to positive. Analyze the intervals of positivity and negativity in the graph of \( g' \).

Suppose g be the continuous function and g' be the derivative of the function g. Critical point: The…

Answered: Suppose g is a continuous function on…

Suppose g is a continuous function on the interval (-5, 4). The graph of g', the derivative of g, is given in the figure below.

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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