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Answer on Calculus Question for hsd

Question #17681
Consider the function f(x)=(3x+6)/(3x+2). For this function there are two important intervals: (−∞,A) and (A,∞) where the function is not defined at A. Determine A.


For each of the following intervals, tell whether f(x) is increasing (input INC ) or decreasing (type in DEC ).


Note that this function has no inflection points, but we can still consider its concavity. For each of the following intervals, tell whether f(x) is concave up (input CU ) or concave down (type in CD ).

Expert's answer
we find A from denominator cant be zero so
3x+2=0 so
x=-3/2 A=-3/2
x not=A so f DEC on the both (−∞,A), (A,∞):
f"=72/(3x+2)^3x belongs (−∞,A) f"<0 then CU
x belongs (A,∞) f">0 then CD

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