Below you are given a function f(x) and its first and second derivatives. Use this information to solve the following.

Question

anonymous · Answer

what is the function?

anonymous · Answer

ok

anonymous · Answer

Determine the intervals where the function is concave up and concave down.

anonymous · Answer

$$f(x) = (x^2 - 4)/(x^2 +1)$$$$f'(x) = 10x/(x^2 +1)^2$$$$f''(x) = 10(1-3x^2)/(x^2 +1)^3$$

anonymous · Answer

for the first one the lowest point is at 
y=-4

anonymous · Answer

at f(0) i got that, isn't there a rule having to do with the second derivative i can 
use?

anonymous · Answer

Are you thinking of  Leibniz's notation?

agent0smith · Answer

Use the second derivative to find concavity. 

It's concave down where f'' is negative, ie f'' < 0

Concave up where f'' is positive, f'' > 0

Find where f'' = 0 firstly.

anonymous · Answer

f' is equal to 0 when x is 2

anonymous · Answer

@Jgeurts

anonymous · Answer

oh i see

anonymous · Answer

i got negative concavity for both sides of zero in [-2,3]

anonymous · Answer

so does that mean it looks something like this? |dw:1367705711666:dw|