standard deviation~10 POINTS

2012-07-21 7:08 pm
Consider the function f(x)= (3x+4)/(4x+3). For this function there are two important intervals:(-infinity,A) and ( infinity,A) where the function is not defined at A.

1. Find A

2.For each of the following intervals, tell whether f(x) is increasing (type in INC) or decreasing (type in DEC).
(-infinity,A) :
(infinity,A) :

3.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 (type in CU) or concave down (type in CD).

(-infinity,A) :
(infinity,A) :

thanks a lot!!!!!!!!

回答 (1)

2012-07-21 9:01 pm
✔ 最佳答案
y = (3x + 4)/(4x + 3) = [3/4(4x + 3) + 7/4]/(4x + 3) = 3/4 + 7/4(4x + 3), so this is the form of a rectangular hyperbola y = c/x shifted upwards by 3/4.
(a) A happens when 4x + 3 = 0, so A = - 3/4.
(b) The function is decreasing for all values of x except at point A. [ dy/dx is negative for all values of x except x = - 3/4].
(c) The function is concave up (opening upwards) when x > -3/4 and concave down (opening downwards) when x < - 3/4.


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