Recent content by sdff22

Thank you very much for he help. So should I consider different cases like: 1. x-->a+ (i.e. x-a>0), then if f(x)>f(a)==>f"'(a)>0 if f(x)<f(a)==>f"'(a)<0 and the same argument for x-->a- (i.e. x-a<0) but I am confused about this fact that having...

F:R-->R, the fourth derivative of f is continuous for all x... Homework Statement Suppose f is a mapping from R to R and that the fourth derivative of f is continuous for every real number. If x is a local maximum of f and f"(x)=0 (the second derivative is zero at x), what must be true of the...

I found it!

f:[a,infinity)-->R is continuous with f(x) > 0 for all x in [a,infinity),... Suppose "a" belongs to R, and f:[a,infinity)-->R is continuous with f(x) > 0 for all x in [a,infinity) and limf(x)=1 (as x goes to infinity). Prove that there exists r>0 such that f(x)>r for all x in [a,infinity).