Question

Help with finding where a f(x) is concave down from derivative graph and inflection points?

Answer 1

wherever the derivative graph has 0 slope or infinite slope, those are your inflection points.
if the derivative graph has a positive slope in that interval and the derivative graph crosses the x axis, it will be concave up in that interval and have a minimum at the x intercept.

i could go on and on but it's a lot to type and you should really look at examples.

give this a shot and see if it helps to explain more thoroughly

Answer 2

http://tutorial.math.lamar.edu/Classes/CalcI/ShapeofGraphPtI.aspx