Let f(x)=(x+3)/kx-2, where x is not equal to 2/k and k is a non zero constant. Let C be the curve y=f(x) with horizontal asymptote y= -1
a. write down the value of k
b. write down the equation(s)of the vertical asymptote(s) of C
c.Find f '(x) and hence find the range of x for which f(x) is increasing.
數學differentiation
2011-12-10 8:01 pm
回答 (1)
2011-12-10 8:56 pm
✔ 最佳答案
(a) f(x) = (x + 3)/(kx - 2) = (1 + 3/x)/(k - 2/x)Let x -> infinity => k = -1
(b) f(x) = (x + 3)/(-x - 2)
So, the vertical asymptote of C is x = -2
(c) f(x) = -(x + 3)/(x + 2)
f'(x)
= - [(x + 2) - (x + 3)]/(x + 2)^2
= 1/(x + 2)^2
So, the range of x for which f(x) is increasing are (-infinity,-2),(-2,infinity)
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