If (x,y) is a point on the graph of a function and f ' '(x) = 0, then (x,y) must be

A An inflection point
B An x-intercept
C A relative extreme
D A critical point

Question

If (x,y) is a point on the graph of a function and f ' '(x) = 0, then (x,y) must be

	A	An inflection point
	B	An x-intercept
	C	A relative extreme
	D	A critical point

anonymous · Answer

i got A?

amistre64 · Answer

its a critical point; f'' = 0 is not sufficient for inflection

amistre64 · Answer

when derivatives are undefined or 0; they are critical points to test out

inkyvoyd · Answer

@amistre64  is correct.

anonymous · Answer

Amistre's right. And inflection point is when the derivative goes from negative to positive. If this happens, then it will be at a point where the second derivative is 0. However, you can't say that if the second derivative is 0 then it will happen.

anonymous · Answer

Assuming the function is continuous and differentiable:
Statement A: f''(a) = 0
Statement B: a is an inglection point of f

B->A
A does not imply B.

anonymous · Answer

thank you! :)

experimentx · Answer

looks like i need to see things back ... LOL

anonymous · Answer

Haha easy mistake, Experiment. I made this mistake myself recently while going over my AP calc student's test.

amistre64 · Answer

mistaken ideas are just important as valid ideas :)

anonymous · Answer

I'm still suffering from online Calculus. :(

amistre64 · Answer

spose f'' = (x+2)^2 

this is zero at x=-2, but it has the same sign on each side of -2 so it is NOT an inflection