Let f: [0, +oo] of all real numbers be differentiable with f(0)=A>0 and f'(x)<= 0 for all x>0

(a) show that there exists some c of (0, +oo) such that f(c)=c

(b) show that there is only one such c

(Note: These facts are obviously intuitively, as you can see be drawing a graph showing the curve y=f(x) and the 45-degree line y=x. The problem is to prove them analytically, using theorems. Since f'<= 0, what do we know about f? Let g(x)=f(x)-x. What do we know about g(0) and g(2A)? What do we know about g'? )