Sketch the graph of a function f that is continuous on [1,5] and has the given properties:(adsbygoogle = window.adsbygoogle || []).push({});

f has no local maximum or minimum, but 2 and 4 are critical numbers.

my professor drew a constant function (horizontal line) from x=1 to x=5. How come there is no local maximum or minimum for a horizontal line? My professor said that all the values of a horizontal line are the absolute maxima and minima...

According to my book, "A function f has a local maximum at c if f(c) >= f(x) when x is near c. [This means that f(c) >= f(x) for all x in some open interval containing c.]" Let's say the open interval is (1,5), and since f(x)=f(c) (because we have a horizontal line), shouldn't f have a local maximum????

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Local max/min

**Physics Forums | Science Articles, Homework Help, Discussion**