Problem

Prove Fermat's Theorem for the case in which $f$ …

06:13

Problem 78 Hard Difficulty

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

Answer

See solution

More Answers

01:07

Wen Z.

Topics

Derivatives

Differentiation

Volume

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 1

Maximum and Minimum Values

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Video Transcript

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

Amrita B.

Topics

Derivatives

Differentiation

Volume

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 1

Maximum and Minimum Values

Top Calculus 2 / BC Educators

Anna Marie V.

Campbell University

Caleb E.

Baylor University

Samuel H.

University of Nottingham

Michael J.

Idaho State University