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Problem :
Find the derivative of the function f (x) = 5x + 2000.
Since this is a line with slope 5, the derivative of f is equal to 5 at
every point, i.e. f'(x) = 5. Note that the constant term does not affect the value of the
derivative. This is the case for any function.
Problem :
Find all functions f such that f'(x) = 0.
The condition f'(x) = 0 implies that the function must have graph with horizontal tangent
at every point. The only possibility is for the graph to be a horizontal line itself.
Thus the function must be f (x) = c for some constant c.
Problem :
Sketch the graph of the derivative of the function f (x) with the following graph:
Figure %: Plot of f (x)
