just want to make and check if this is right or not?

Question

http://i181.photobucket.com/albums/x85/ctti_3/untitled-24.jpg

f is concave down on (-inf, 0) would that be true even if there's a 0 (1st deriv) at x=-3
then the answer would be all true?

Answer 1

Yes, that is true; even if the "0" is at -3 the entire graph of f can still be concave down on (-inf, 0).

Found this at:

http://www.sosmath.com/calculus/diff/der15/der15.html

check the red function on the second graph on the page. This could be like your f but shifted a little to the left.

Answer 2

y" changes its sign from - to + as it passes through x=0 so it has a point of inflection there.