Calculus

Answer the following questions for the function f(x)=(x^3-9x^2+27x-27)/(x^2-6x+8) defined on the interval [-14, 22].

Enter points, such as inflection points in ascending order.

A. The function f(x) has vertical asymptotes at _______ and ________.

B. f(x) is concave down on the region ________ to __________ and __________ to ________.

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  1. since the denominator is zero at x=2,4 A is easy to answer

    concave down when f" < 0
    f" = 2(x^3-9x^2+30x-36) / ((x^2-6x+8))^3
    The numerator is positive for x>3 and negative for x<3

    The denominator is positive for x<2 and x>4

    f" < 0 for x<2 and 3<x<4

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