Absolute Maximum and Minimum Values (VCE SSCE Mathematical Methods): Flashcards

Highest value function reaches on its domain

Lowest value function reaches on its domain

Stationary pts, endpoints, where derivative doesn't exist

$f(x) \leq M$ for all $x \in [a,b]$

$f(x) \geq N$ for all $x \in [a,b]$

All critical points and both endpoints

Can change where absolute max/min occurs

Variation table or sign analysis of derivative

Absolute extrema will occur at an endpoint

Not always at stationary pts; can be at endpoints too