Calculus: Early Transcendentals, 8th Edition
Authors: James Stewart
ISBN-13: 978-1285741550
See our solution for Question 4E from Chapter 2.8 from Stewart's Calculus, 8th Edition.
Problem 4E
Chapter:
Problem:
Trace or copy the graph of the given function f. (Assume that the axes have equal scales.) Then...
Step-by-Step Solution
Given information
We are given with following graph
https://imgur.com/P0yfH61
We have to find graph of its derivative. To plot the graph we have to find slopes of tangent at number of points and join them.
Step 1: Slopes at local maxima and minima
There are three points as shown in the Figure above where the slope is zero. That means graph of the derivative will pass x axis at these three points.
Step 2: Slope from $ - \infty $ to P
From the graph, we can see that slope till point P is negative and becomes zero at P.
Between p and Q, it becomes positive, as the function is increasing. The rate of slope is positive in the beginning and then becomes negative.
Step 3: Slope from Q to $ + \infty $
As the function is symmetric about y axis, the derivative is symmetric about origin.
Step 4: The plot is shown below
https://imgur.com/khcYw91
We are given with following graph
https://imgur.com/P0yfH61
We have to find graph of its derivative. To plot the graph we have to find slopes of tangent at number of points and join them.
Step 1: Slopes at local maxima and minima
There are three points as shown in the Figure above where the slope is zero. That means graph of the derivative will pass x axis at these three points.
Step 2: Slope from $ - \infty $ to P
From the graph, we can see that slope till point P is negative and becomes zero at P.
Between p and Q, it becomes positive, as the function is increasing. The rate of slope is positive in the beginning and then becomes negative.
Step 3: Slope from Q to $ + \infty $
As the function is symmetric about y axis, the derivative is symmetric about origin.
Step 4: The plot is shown below
https://imgur.com/khcYw91