Question

3. Discuss the graph of y=x/3+2+3/x. Determine the values of x for which the graph is
a. Continuous
b. Rising
c. Falling
d. Concave upward
e. Concave downward
f. Has a relative maximum
g. Has a relative minimum

Answer 1

If you combine terms you see that it's just

y = (x+3)^2/3x
y' = 1/3 - 3/x^2
y'' = -6/x^3

Continuous except where denominator is zero

rising/falling where y' is positive/negative

concave up where y'' > 0

max/min where y' = 0

Answer 2

Oops

y'' = 6/x^3