is it possible to have a function which has a sharp turn and yet when you take the second derivative it reduces down to a polynomial.

the original question is F''=2x-12 with a max/min critical point at x=4. and they want to know if its a min or max without knowing the original function. so if you check both sides of x=4 its concave down for both regions. but my argument is that just because its concave down does not mean its a max because what if its both concave down and yet a min with a sharp turn.

so can we determine that F''=2x-12 was actually derived from a smooth polynomial or co

Question

is it possible to have a function which has a sharp turn and yet when you take the second derivative it reduces down to a polynomial. 

the original question is F''=2x-12 with a max/min critical point at x=4. and they want to know if its a min or max without knowing the original function. so if you check both sides of x=4 its concave down for both regions. but my argument is that just because its concave down does not mean its a max because what if its both concave down and yet a min with a sharp turn. 

so can we determine that F''=2x-12 was actually derived from a smooth polynomial or co

misty1212 · Answer

HI!!

misty1212 · Answer

what does " it reduces down to a polynomial. " mean?

fellowroot · Answer

could the original function actually not be a polynomial and contain a sharp point yet we can't tell from looking at the F'' because maybe terms cancelled out after taking the derivative and so we only see a polynomial.

fellowroot · Answer

by reduce i mean. you have a function and take the derivative and when you collect like terms and such part of it goes away. (cancels)

fellowroot · Answer

actually i think yes, because if you look at |x| function it has a sharp point yet when you find derivative at least if you consider a certain interval it reduces down to a function that doesnt have a sharp turn