I am having trouble on this practice problem.I keep getting upside down parabola but I dont think that is right. **Classwork Session 4 Practice Problems:**1. The graph below shows the graph $ y = f(x) $ of a function $ f(x) $. Sketch the graph $ y = f'(x) $ of the derivative. (Hint: think about where $ f'(x) $ is positive, negative, or zero; and think about where it is large in magnitude or small in magnitude. Do not try to do it algebraically, by guessing a formula for the function being graphed here.)**Graph Explanation:**The graph provided is a continuous curve representing the function $ f(x) $. Here are important features to consider when sketching the derivative $ f'(x) $:- **Critical Points:** Identify where the slope of the graph (tangent) is zero. These are points where the curve changes direction (peaks and troughs).- **Increasing/Decreasing Intervals:** Determine where the function is increasing (positive slope, $ f'(x) > 0 $) and where it is decreasing (negative slope, $ f'(x) < 0 $).- **Concavity and Inflection Points:** Consider where the curve changes concavity. Inflection points will not be evident in the derivative sketch if you only look for zero slope points but observe changes in curvature to build an accurate intuition.- **Magnitude of Slope:** Notice sections where the curve is steep (greater magnitude of $ f'(x) $), both positive and negative, compared to flatter areas (smaller magnitude of $ f'(x) $).Using these observations, sketch the derivative graph, which visually represents the rate of change of the function.

Classwork Session 4 Practice Problems: (1) The graph below shows the graph y = f(x) of a function f(x). Sketch the graph y =f 0 (x) of the derivative. (Hint: think about where f 0 (x) is positive, negative, or zero; and think about where it is large in magnitude or small in magnitude. Do not try to do it algebraically, by guessing a formula for the function being graphed here.) %3D

Classwork Session 4 Practice Problems: (1) The graph below shows the graph y = f(x) of a function f(x). Sketch the graph y =f 0 (x) of the derivative. (Hint: think about where f 0 (x) is positive, negative, or zero; and think about where it is large in magnitude or small in magnitude. Do not try to do it algebraically, by guessing a formula for the function being graphed here.) %3D

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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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

Question

I am having trouble on this practice problem.

I keep getting upside down parabola but I dont think that is right.

**Classwork Session 4 Practice Problems:**

1. The graph below shows the graph $ y = f(x) $ of a function $ f(x) $. Sketch the graph $ y = f'(x) $ of the derivative. (Hint: think about where $ f'(x) $ is positive, negative, or zero; and think about where it is large in magnitude or small in magnitude. Do not try to do it algebraically, by guessing a formula for the function being graphed here.)

**Graph Explanation:**

The graph provided is a continuous curve representing the function $ f(x) $. Here are important features to consider when sketching the derivative $ f'(x) $:

- **Critical Points:** Identify where the slope of the graph (tangent) is zero. These are points where the curve changes direction (peaks and troughs).

- **Increasing/Decreasing Intervals:** Determine where the function is increasing (positive slope, $ f'(x) > 0 $) and where it is decreasing (negative slope, $ f'(x) < 0 $).

- **Concavity and Inflection Points:** Consider where the curve changes concavity. Inflection points will not be evident in the derivative sketch if you only look for zero slope points but observe changes in curvature to build an accurate intuition.

- **Magnitude of Slope:** Notice sections where the curve is steep (greater magnitude of $ f'(x) $), both positive and negative, compared to flatter areas (smaller magnitude of $ f'(x) $).

Using these observations, sketch the derivative graph, which visually represents the rate of change of the function.

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