Indeed, the derivative is .
If x is a critical point then . (1)
The oblique asymptote is where and .
Now, .
(2)
From (1) and (2) we get:
I) point of minimum
II) point of maximum.
This is the function:
f(x)=(x^2-Bx+4)/(x-A)
given:
x=2 critical point
y=x+5 is an oblique asymptote
I need to find A and B and decide if x=2 is min or max.
i got to f'(x)= (x^2-2Ax-4+BA)/{(x-A)^2}
but I'm not even sure that I need a derivative here.
can someone explain what would be the way to solve this?
Please, if you can, show your work so that I can understand it.
THANKS!