Draw the graph of a functionfsuch thatf′(x)<0 andf′′(x)>0 for allxinthe interval (0,5). Label the axes and mark the points on thexaxis which correspond to 1and 5.

Answer 1

f ' (x) < 0 means that f has negative slopes... which means f is decreasing.

f '' (x) > 0 means that f ' (x) is increasing (bc it has positive slopes) which means that f(x) is concave up.

So, you need to draw a decreasing function that is concave up! (think about a concave up parabola-- which half is decreasing?)