# Applications of Differentiation

**Application of Differentiation**

- The Extreme Value Theorem

If f is continuous on a closed interval [a,b], f has an absolute max value f(c)and absolute min value f(d) at c and d in the interval [a,b]

- Fermat's Theorem

If f has a local max or min at c, and f'(c) exists, f'(c)=0

- Critical Number

A number c in the domain of f such that f'(c)=0 or f'(c) doesn't exist

- Closed Interval Method

y=x^{2}
Minimum value:0; No Maximum Value

y=x^{3}
No minimum value; No maximum value

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