Question 1209599
<pre>
D(x) = sin(|x|)

Concave upward means like a U. 

Absolute values are always positive or zero.  So in D(x), we are always taking
sines of positive or zero numbers, so D(x) will only be concave upward when the
sines of positive numbers or zero are negative or zero.  This only occurs in
quadrants 3 and 4. 

All choices except 2.

Answer: choices 1, 3, and 4.

{{{drawing(400,200,-4pi-1,2pi+1,-1.5,1.5,

line(-4pi,-.8,-4pi,.3),locate(-4pi-1,-.8,-4pi),
line(-3pi,-.8,-3pi,.3),locate(-3pi-1,-.8,-3pi),
line(-2pi,-.8,-2pi,.3),locate(-2pi-1,-.8,-2pi),
line(-pi,-.8,-pi,.3),locate(-pi-1,-.8,-pi),
line(2pi,-.8,2pi,.3),locate(2pi+.1,-.8,2pi),
line(pi,-.8,pi,.3),locate(pi-.2,-.8,pi),

locate(-11.65,-.3,YES), locate(-11.65+2pi,-.3,YES),

locate(10.65-2pi,-.3,YES), locate(-2,.4,NO),

graph(400,200,-4pi-1,2pi+1,-1.5,1.5,sin(abs(x))))}}}

Edwin</pre>