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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