what are the key Points of f(x)= 1/x^2-9 and 𝑓(𝑥)= 𝑥+2/ 𝑥^2−5𝑥+4

Answer 1

f(x) = (x+2)/(x^2 -5x+4) = (x+2)/(x-4)(x-1)

It graphically has vertical asymptotes at x-1 and x=4, a horizontal asymptote y=0

y intercept is (-2,0)

no global max or min

local max about (2.6, -2)

local min about (-2.1, 0.005)

discontinuous at x=1, x=4

concave up for x<1 and x>4

concave down for 1<x<4

f(x) = 1/(x^2-9) = 1/(x+3)(x-3)

horizontal asymptote is y=0 or the x axis

vertical asymptotes at x=-3 and x=3

no global max or min

local max is (0,-1/9)

concave up everywhere except -3<x<3