Question

find on what intervals function is concave up or down.
f(x)=x^3
so f''(x) = 6x

Answer 1

So what do you use the second derivative for? That's the change of the change in the function right? The second derivative is basically just telling you how it's changing. In order to reverse the direction it's changing (going from concave down to up or the other way around) we need to go through 0! This is called an inflection point, so are there any here?

Answer 2

Concave up will have the second derivative negative

Answer 3

how will i figure if its concave up or down? its - if less than 0 and + if more than 0

Answer 4

@kc_kennylau are you sure?

Answer 5

mean value theorm says to find second derivative

Answer 6

@Kainui well... no.

Answer 7

The second derivative will only tell you how it's changing slope. It won't tell you whether the slope is up or down though. In this case the slope is increasing by 6 for every 1 step you move to the right.

Answer 8

A nice way to think about concavity as if it's the acceleration. Is it accelerating upwards or downwards?

Answer 9

ok so if x is - then its concave up
and x=+ concave down

Answer 10

am i right ?

Answer 11

Nope. Other way around.

Answer 12

u said concave up will have second derivative negative ?

Answer 13

????

Answer 14

When the second derivative is -, <0, it's concave down. I like to use <0 or >0, because the less than or greater than signs give the shape of the 'cave' :DD

Answer 15

When you tilt your head to the left, lol. Anyone else do this, :D :D :D. No..Ok.