{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

11.10 - Section 4.1 Key concepts Absolute(or global vs...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Section 4.1 : Key concepts? ..?.. Absolute (or global) vs. relative (or local) maxima and minima, critical numbers A function f with domain D has a global maximum at c if f ( c ) f ( x ) for all x in the domain of f . We call f ( c ) the maximum value of f on D . We say f has a local maximum at c if f ( c ) f ( x ) for all x in some suitably small neighborhood of c (note: this requires that f ( x ) is defined in some neighborhood of c , so that in particular c cannot be an endpoint of D ). Global and local minima are defined in the same way, using instead of . Note that the function f ( x ) = x with domain [0,1] has no local maximum or minimum! It does however have a global maximum (at c =1) and a global minimum (at c =0).
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 The function f ( x ) = x with domain (0,1) has no global or local maxima or minima! Ditto for the function f ( x ) = x with domain R . The function f ( x ) = cos x with domain R has global maxima at all points c =2 π n ; it also has local maxima there.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}