The graph of y=-5/x-2 is concave downward for all values of x such that x=?

Question

Its a multiple choice question

x<0

x<2

x<5

x>0

x>2

Answer 1

The graph of y=f(x) is concave down when the derivative f’(x) is decreasing or equivalently when the second derivative f”(x)<0. In this case f(x)=-(5/x)-2 so f’(x)=5/x^2 and f”(x)=-10/x^3 and hence f”(x)<0 if and only if x<0. Answer: x < 0.