Question

can we assume no concavities for any function that the power is smaller than x^3? so any function with x^2 would have no concavities?

Answer 1

is x^2 a line or a curve?

Answer 2

curves by default have concavity; lines do not

Answer 3

aren't all x^2 a curve because they are parabolas?

Answer 4

yep

Answer 5

the reason why I asked the first question is because in order to find concavities we need to find the second derivative right?

Answer 6

"need" ?? nah .... but if you want to go that route then fine

Answer 7

haha ok imma keep it simple for myself and still go this route

Answer 8

but when I go this route... for an example like this: (x^2)-3. the second derivative becomes 2.

Answer 9

this is where its throwing me off.

Answer 10

f(x) = x^2 + 6x + 12

f' = 2x + 6

f'' = 2 is a positive value always so this tells us that an +x^2 is always cave up

Answer 11

the points where the concavity changes would possible at f'' = 0 or undefined

Answer 12

hmm ok.. so if my second derivative is just a constant, then its showing me that its always that way no matter what the x is right?

Answer 13

correct; and since the sign demonstrates if its up or down ... +2 is always a cave-up concavity

Answer 14

so the question is asking me to find intervals of the concavity.

Answer 15

they gave me my closed intervals of (0<or equal to x <or equal to 2

Answer 16

so should I just assume that because they gave me those intervals I can say from 2,infinity concave up?

Answer 17

can you show me a pic of it?

Answer 18

they never gave me a picture. or are you asking for the picture of the original graph? I can get that from wolfram...

Answer 19

is the original question asking you for the concavity between 0 and 2 ?

Answer 20

yes.

Answer 21

then its concavity up between 0 and 2; just not too sure how to format that to your solution

Answer 22

if this had to do with a program; then i was asking if you could take a screenshot of the problem to see if i could understand what sort of format they might want is all

Answer 23

yeah... it really doesn't have much info haha but thank you! :)