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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

The figure shows the graphs of f, f', and f". Identify each curve, and explain your choices.

Chapter 2, Problem 48RE, The figure shows the graphs of f, f', and f". Identify each curve, and explain your choices.

To determine

To Identify: The curves f,f and f on given with proper explanation.

Explanation

Graph:

The given graph is shown as in Figure 1,

Observation:

From the Figure 1, it is observed that the point b(x)=0 is the same point where the graph of c has horizontal tangents.

Recall that the derivative of a function is zero where the function has a horizontal tangent.

Therefore, b(x) is the derivative of the graph c(x). That is, c(x)=b(x).

Observe the graph of a and c carefully.

The slope of the curve is positive for x<0 and the slope is negative for x>0. c is the only curve which is positive or x<0 and negative for x>0

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