question archive Let f(x) be a continuous function on ( -infinity, infinity)

Let f(x) be a continuous function on ( -infinity, infinity)

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Let f(x) be a continuous function on ( -infinity, infinity). Suppose that f'(-1) = 1. Which of the following statements is true:

f has a local maximum at x=-1

f has an absolute maximum at x= -1

f does not necessarily have a local extremum or absolute extremum at x = -1

f has a local minimum at x= -1

f has an absolute minimum at x= -1

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