To find:The one function which is its own derivative.
Answer to Problem 25E
The required function which is its own derivative is the function (iv).
Explanation of Solution
Given information:
The graphs:
(i)
For
(i)
(ii)
(iii)
It is seen that in the functions (i), (ii) and (iii) the graphs have nonzero slopes at
This means none of the above graphs are their own derivative.
For the function (v);
Substitute 1 for x in the function
Differentiate the above function.
Substitute 1 for x in the above function.
Observe that the graph of the function (v) is not its own derivative as y = 1 and
This means the function
Hence, the required function which is its own derivative is the function (iv).
Chapter 3 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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