Sketch the graph of a function
f
with the following properties:
\lim_(x->-\infty )f(x)=\lim_(x->\infty )f(x)=0,f^(')(x)>0
, for
x<0,f^(')(x)<0
, for
x>0
f^('')(x)>0
, for
x<-1,f^('')(x)<0
, for
-10
, for
x>1
Determine nonnegative numbers
x>=0,y>=0
which maximize the product
P=xy
subject to the constraint
x+2y=60
. Use the closed interval method to verify your answer. Please answer both