Question

If f(x) is a twice-differentiable function and f’’(c) = 9 at an interior point c of f’s domain, must f have an inflection point at x = c? Explain.

Answer 1

f(x) has an inflection point at x=c
if and only if
f''(c) = 0

so, what do you think?

Answer 2

Umm idk

Answer 3

what happens when
1) second derivative > 0 ->
2) second derivative < 0 ->
3) second derivative = 0 ->

Answer 4

in > 0 its concave up and < 0 its concave down if its = 0 no concavity or it is a possible inflection point

Answer 5

correct.

so thats the answer.
look at the third one you said and compare it with the given second derivative.

Answer 6

so yes it does have an inflection point

Answer 7

how?
explain your train of thoughts.

Answer 8

never mind i cehcked it doesn't

Answer 9

no solutions exist

Answer 10

the question does not ask for a solution!
but an answer to the question and an appropriate explanation

Answer 11

ohh ok so i could say there is no inflection point at x = c because its equal to 0 and we know when it equals to zero there is not concavity?

Answer 12

the question said,
f''(c)=9
we know that \(9\ne0\) and that \(9>0\).
but for inflexcion point, \(f''(c)\) MUST EQUAL 0
so....

Answer 13

ohh ok

Answer 14

i'm still not getting this

Answer 15

ok, you said that at inflection point, \(f''(x)=0\), right?

Answer 16

yes

Answer 17

good.
and what is the given \(f''(x)\)?

Answer 18

its 9

Answer 19

so.... ?