Conclusion for every even continuous function is the derivative of an odd continuous function and vice versa.
Answer to Problem 78E
We can conclude that every even continuous function is the derivative of an odd continuous function and vice versa.
Explanation of Solution
Given information:
From previous exercises,
For g(-x) = g(x):
For g(-x) = -g(x):
Suppose that f is an even continuous function,
Then
Moreover,
Thus,
In the same way,
Suppose that f is an odd continuous function,
Then
Moreover,
Thus,
Therefore,
We can conclude that every even continuous function is the derivative of an odd continuous function and vice versa.
Chapter 6 Solutions
Calculus: Graphical, Numerical, Algebraic
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