"Don't fear the cereal" was originally going to be the title of Blue Oyster Cult's biggest hit. Then they realized the Grim Reaper was potentially more terrifying than Captain Crunch. True story.

Monty Python's SPAMalot Wins 5, no, 3 Tony Awards

geeks out, dies laughing

I thought I had an answer but was wrong. Anybody?

My best guess would be f(c) = 4, assuming c = 2, but it's just a guess.

I thought I had an answer but was wrong. Anybody?

2

Can you imagine the power of an infinite number of Theremins, bringing down defenses, shattering eardrums.

Somehow "piercing" and "woo-woo-woo" don't quite go together in my mind.

The function f is differentiable on the interval 0 < x < 4. If f(1)=1 and f(3)=7, then for some 1 < c < 3, f'(c) must be equal to:

1, 2, 3, 4, or 6?

3. It's the mean value theorem: for some value on the interval, the slope must be equal to the average slope, which is (7-1)/(3-1) = 3.

Jon, that is just about the sweetest story ever. Even with the Tex Avery moments, just so damn sweet. Millions of congratulations all over again!

haha, I loved the Tex Avery moments.

But fate had other plans and now we have two anniversaries to remember.

I tend to get around this problem by just not remembering them.

OK, there are an infininte number of functions that would fulfill that criteria. The function could be a straight line with slope of 2 3. If not, then say it is a function that has a slope of less than 2 3 for part of that interval. Then another part must have a slope of greater than two, and since it's differentiable then there must also be a point with a slope of 2 3 in there....

3. It's the mean value theorem: for some value on the interval, the slope must be equal to the average slope, which is (7-1)/(3-1) = 3.

Argh!

I get the concept right but flunk on the basic math part!!!!

eta: I drew a little graph but made a mistake - I plotted f(1) = 3 for some reason.....