Question

I need some to double check my conclusions about a second derivative graph and what it tells me about the original function

Answer 1

I need to state all of my conclusions about F(x) and then all of my conclusion about F '(x) using F " (x)

Answer 2

I really meant to use lowercase f not F

Answer 3

For my conclusion about f(x)
If f " (x) is positive then f(x) is concave up

f(x) is concave up from (0,3) and (3, infinity)

Answer 4

For my conclusion about f(x)
If f " (x) is negative then f(x) is concave down

f(x) is concave down from (- infinity, 0)

Answer 5

Point of Inflection occurs when f " (x) changes sign
so f(x) has a point of inflection at x=0

Answer 6

This is where I need my double check, did I make any incorrect statements?

Answer 7

looks good so far :)
u may use graphs to double/triple check your conclusions
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Answer 8

@ganeshie8 Thanks you are awesome :)