Determine the intervals of concavity and inflection points:
i) f(x) = x^3 - 2X
ii) g(x) = x/(x+1)

Question

Determine the intervals of concavity and inflection points: 
i) f(x) = x^3 - 2X 
ii) g(x) = x/(x+1)

anonymous · Answer

Find the second derivative.  Where it is positive, it is concave up; negative, concave down.  The zeros of the second derivative are points of inflection.

anonymous · Answer

Note that in problem b, the change happens at a point where the function is undefined; this is probably not considered a point of inflection.

anonymous · Answer

if f''(x)=0 undefined, meaning no point of inflection? 
if the sign of f''(x) doesnt change for both sides, does it still consider as point of inflection?

anonymous · Answer

$$f(x) = x^3 - 2x \implies f"(x)=6x \implies x=0~inflection~point$$Since f" is negative for x<0, it is concave down in that area, concave up for x>0.