I've come to a few assumtions that my text hasn't covered yet, and I was hoping someone could confirm these for me or let me know where I might be missing something.(adsbygoogle = window.adsbygoogle || []).push({});

Assuming f is an odd function and a > 0 and b > 0 and a < b:

If f'(x) > 0 on (a,b), then f'(x) < 0 on (-b,-a).

If f''(x) > 0 on (a,b), then f''(x) < 0 on (-b,-a).

If lim (x->a) f(x) = inf, then lim (x->-a) f(x) = -inf

If x = a is a vertical asymptote of f, then x = -a is also a vertical asymptote of f.

If lim (x->inf) f(x) = L, then lim (x->-inf) f(x) = -L

If y = L is a horizontal asymptote of f, then y = -L is also a horizontal asymptote of f.

If f is odd and f is continuous on (-a,a), then f(0) = 0

Thanks,

hk

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# Derivatives of an odd function

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