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If a differentiable f has a local extremum at an interior point c, then
Af(c) = 0
Bf'(c) = 0
Cf'(c) = 1
Df''(c) = 0
Answer & Solution
Correct answer: B. f'(c) = 0
At a smooth hilltop or valley bottom the tangent is horizontal, so the slope is zero.
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