Question

Calculus points of inflecion help??

determine whether the
statement is true or false. If it is false, explain why or give an example that shows it is false

If f'' (2)=0, then the graph of f must have a point of inflection at x=2.

I think it is true. Am I correct?

Answer 1

I think its true too

Answer 2

false. By definition, an inflection point is where a function changes it's concavity
Consider, y = x^4
f''(0) = 0, but there is no change in concavity. In fact, x^4 is always concave up

Answer 3

I'm pretty sure an inflection point is simply where the function `can` change concavity.. i better look that up though.

Answer 4

No I guess I've forgotten a few things haha XD
Ya I guess it has to change signs.

Answer 5

Lemme erase all that garbage from before so I don't confuse you hehe

Answer 6

what you need to for a point of inflexion is

1. Solve the 2nd derivative, this MAY give a point of inflexion.

2. test either side of the point, looking for a change in sign, which means a change in concavity...

hope this helps..

Answer 7

to me, it's true

Answer 8

I don't have a function so I can't try and solve it myself.... I'm confused. :(

Answer 9

well that statement is false... as you need to test either side of the solution to see if there is a change in concavity.

Answer 10

ok. thank you everyone @koymoi @sourwing @campbell_st @Loser66 @zepdrix