"Does there exist a function such that f(0)=-1, f(2)=4, and f'(x) is less than or equal to 2, for all x?"

I have no idea of how to solve or go about starting this problem, other than guess and check... Can someone walk me through this one?

Any and all help is greatly appreciated!

Question

"Does there exist a function such that f(0)=-1, f(2)=4, and f'(x) is less than or equal to 2, for all x?"

I have no idea of how to solve or go about starting this problem, other than guess and check... Can someone walk me through this one?

Any and all help is greatly appreciated!

anonymous · Answer

mean value theorem 
you can do it in your
e head

anonymous · Answer

at time $t=0$ you are at mile marker $-1$ 
you speed limit is $2$ miles per hour
can you get to mile marker 4 in two minutes?

anonymous · Answer

or rather two hours

anonymous · Answer

the answer is no, because you cannot go 5 miles in two hours if your speed limit is two miles per hour 
we can do it the math teacher way if you like

amonoconnor · Answer

No, I think I get it.. that's so much easier than I ever could have imagined. And not just easy, but it's like... clear. Lols, Thank you:)