Unit 5 : Applications Of Derivatives

Mean Value Theorem

Mean Value Theorem

Extreme Value Theorem

Extreme Values

The minimum and maximum of a function on an interval.

Can occur at end points or interior points

Relative Extrema

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

How do you find a critical point?

Candidates Test

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

When f prime = 0

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)