Thread: Quick Question about Vertical Asymptotes

Hi guys I am computing the derivative to check the intervals of increase/decrease of my given function. I was just wanting to know when I check the vertical asymptote in the denominator would I check in the original function f(x)'s denominator or f'(x) 's denominator after I differentiate. Then when I am check concavity should I check the denominator of f(x) f'(x) or f''(x). I am just looking for a bit of clarification.


Thanks

qbkr21

Originally Posted by qbkr21

Hi guys I am computing the derivative to check the intervals of increase/decrease of my given function. I was just wanting to know when I check the vertical asymptote in the denominator would I check in the original function f(x)'s denominator or f'(x) 's denominator after I differentiate. Then when I am check concavity should I check the denominator of f(x) f'(x) or f''(x). I am just looking for a bit of clarification.


Thanks

qbkr21

f'(x) always gives the slope properties.
f''(x) always gives the concavity.

And if y = f(x) has a vertical asymptote at a point x = x0, then any derivative of f(x) will also display that asymptote.

I think I answered your question. Let me know if I didn't.

-Dan

RE:

Thanks!!!

Ahhhh...But the denominators of f'(x) and f''(x) must be included as Critical Points...on the # test line.