Calculus

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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

  • Calculus -

    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

  • Calculus - PS -

    Oops

    y'' = 6/x^3

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