Prove that, if f'(x) exists and is continuous on an interval l and if f'(x) 0

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Prove that, if f'(x) exists and is continuous on an interval l and if f'(x) ≠ 0 at all interior points of l, then either f is increasing throughout l or decreasing throughout l.
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Calculus

ISBN: 978-0131429246

9th edition

Authors: Dale Varberg, Edwin J. Purcell, Steven E. Rigdon

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