# Answer to Question #17681 in Calculus 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.

A=

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

(−∞,A):

(A,∞):

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 ).

(−∞,A):

(A,∞):

A=

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

(−∞,A):

(A,∞):

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 ).

(−∞,A):

(A,∞):

Expert's answer

we find A from denominator cant be zero so

3x+2=0 so

x=-3/2 A=-3/2

f'=-12/(3x+2)<0

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

3x+2=0 so

x=-3/2 A=-3/2

f'=-12/(3x+2)<0

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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