calculus i review

key term - Fermat’s theorem

Definition

Fermat's theorem states that if a function has a local maximum or minimum at some point, and the derivative exists at that point, then the derivative must be zero. It is essential for finding critical points in calculus.

5 Must Know Facts For Your Next Test

  1. Fermat's theorem applies to differentiable functions.
  2. If $f'(c)=0$, then $c$ is called a critical point.
  3. Critical points are potential locations for local maxima and minima.
  4. The theorem does not guarantee that a function with $f'(c)=0$ has a local extremum at $c$; it only indicates potential extremum points.
  5. To determine if a critical point is an actual maximum or minimum, further tests like the second derivative test may be required.

Review Questions

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