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If $f$ has a local minimum value at $c$, show that the function $ g(x) = - f(x) $ has a local maximum value at $c$.

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01:07

Wen Zheng

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 1

Maximum and Minimum Values

Derivatives

Differentiation

Volume

Harvey Mudd College

Baylor University

University of Nottingham

Boston College

Lectures

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okay, We know that the derivative of negative FX is negative to the original parent function, which is FX. Therefore, we know the local maximum is a point in this context, and we know it's the point where the function changes from increasing to decreasing and the local minima, by contrast, is where function changes from decreasing to increasing. We know the function is decreasing before X equal, see and increasing just after x equal. See, we know that increasing and decreasing behaviors opposite. Therefore, we note there Haas to be a local maximum at X equal, see

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