f(x)=2x+8x^-1.For this function there are four important intervals: (-infinity,A],[A,B),(B,C), and [C,infinity) where A,B and C are either critical numbers or points at which f(x) is undefined.Find A,B and C.

Question

f(x)=2x+8x^-1.For this function there are four important intervals:         (-infinity,A],[A,B),(B,C), and [C,infinity) where A,B and C are either critical numbers or points at which f(x) is undefined.Find A,B and C.

Reiny · Answer

f'(x) = 2 - 8/x^2
setting this equal to zero yields x = ±2
where y is then ±8

I will describe the function:
Vertical asymptote at x = 0
Minimum point at (2,8)
Maximum point at (-2,-8)
Oblique asymptote y = 2x