Concavity i get!!!!

1. the function is increasing at (-2,0)U(o,2) because all the out puts are Positive!
(&= infinity... hahah couldn't find the symbol)
The funcion is decreasing at (-&, -2)U(2,&) because all the outputs are negative!

i can tell because i use the ARROW test . if the arrow is going up to get to the output its positive, if the arrow is going down to its utput its negative

2. the etremas are at x=-2,0,2 because at those points at output is zero. since the derivative is the slope then its when there is a change from + to - or the other way around.

3. Using the derivative, the function is concave up at (-&, 1.30)U(0,&). we know this because of the concavity test which said if f '' (x) >0 its concave up (the slope is increasing f '(x))!
its concave down at (-1.30,0)U(1.30,&) because the slope is decreasing.

with the graph i can tell because if it holds water its concave up and if it spills water its convace down
concavity test!

4.i drew it on a paper and it looks like f '(x) = x^4 so i think the function is (x^5)/5 because if you do the chain rule it would bring down the exponent(5) and multiply it with the coefficient of the variable wich is (1/5) and then that would become 1 . then you take the exponent that it had (5) and subtract by 1. your left with x^4.