If f is a continuous, decreasing function on [0,10] with a critical point at (4,2), which of the following statements must be false?
A f(10) is an absolute minimum off on [0, 10]
B f(4) is neither a relative maximum nor a relative minimum.
С f(4) does not exist
D f'(4) < 0
Homework Answers
A. f(10) is an absolute minimum of f on interval [0, 10]
It is so since f is a continuous decreasing function on interval [0, 10].
At point (4, 2) it will be an inflection point so the decreasing feature continues after that critical point.
Option D is the answer
ie. Option D is false
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