Unit 5 : Applications Of Derivatives

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8 Terms

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Mean Value Theorem

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2
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Extreme Value Theorem

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Extreme Values

The minimum and maximum of a function on an interval.

Can occur at end points or interior points

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Relative Extrema

Local Max and Local Min, can’t be end points

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How do you find a critical point?

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6
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Candidates Test

Critical Points and End Points, Used for finding Max And Min

When f prime = 0

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Point Of Inflection

f’’ changes sign at x=c and where f changes concavity

Where f’’ = 0 or f’’ does not exist

COMMON MISTAKES

Assuming that f’’ = 0 means there is a POI check if it changes sign

Assuming that f’’ ≠ 0 means there is no POI , f(c) has to be defined so if its f’’ doesn't exist it has to spit out a value for f(c)

<p>f’’ changes sign at x=c and where f changes concavity</p><p>Where f’’ = 0 or f’’ does not exist</p><p><mark data-color="yellow">COMMON MISTAKES</mark></p><p><mark data-color="purple">Assuming that f’’ = 0 means there is a POI check if it changes sign</mark></p><p><mark data-color="purple">Assuming that f’’ ≠ 0 means there is no POI , f(c) has to be defined so if its f’’ doesn't exist it has to spit out a value for f(c) </mark></p>
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