T/F There exists a function f f such that f(x)<0 f ( x ) < 0 , f'(x)<0 f ′ ( x ) < 0 , and f''(x)>0 f ″ ( x ) > 0 for all real numbers x x .

Question

There exists a function  such that , , and  for all real numbers .

Answer 1

Nothing is said about continuity....

f(x) =

1/x for x<= -1

-(x+1)^3-1 for -1 <x <0

-sqrt(x)-2 for x>=0