Let and , where . If attains its maximum value at and attains its minimum value at ,…

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

Let

f(x)=5-|x-2|

and

g(x)=|x+1|

, where

x\in\mathbb{R}

. If

f(x)

attains its maximum value at

\alpha

and

g(x)

attains its minimum value at

\beta

, then

\lim_{x\to-\alpha\beta}\frac{(x-1)(x^2-5x+6)}{x^2-6x+8}

is equal to (a)

\frac12

(b)

-\frac32

(c)

-\frac12

(d)

\frac32