Find the open intervals on which
y = x + (4/x)
is increasing.
A. On (−2, 2)
B. On (−∞, 0) and on (0,3/2)
C. On (−2, 0)
D. On (−∞, −2) and on (2, ∞)
E. None of these
F. On (−∞, −2) and on (−2, 1)

Question

Find the open intervals on which
y = x + (4/x)
is increasing.
A. On (−2, 2)
B. On (−∞, 0) and on (0,3/2)
C. On (−2, 0)
D. On (−∞, −2) and on (2, ∞)
E. None of these
F. On (−∞, −2) and on (−2, 1)

owlcoffee · Answer

$$y= x+ \frac{ 4 }{ x }$$
Try first making all this into one fraction using common denominator:
$$y= \frac{ x ^{2}+4 }{ x }$$
Now, in order to see much clearer we must study it's sign, and then it's derivatives.

owlcoffee · Answer

If I'm not wrong, the derivatives of a function mark us the increasing or decreasing behavior in a function.
What values of x can't the function take?

ranga · Answer

First note that this function is not defined for x = 0.  All other values of x are okay.
y = x + 4/x

Find the derivative, equate it to zero and solve for x.  Those are the critical points.  Put the values in and see if it is a maxima or a minima.  Then you can find the intervals in which the function is increasing.