Is #f(x)=(x^2-6x-12)/(x+2)# increasing or decreasing at #x=1#?

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Answer 1 · 2016-03-13T23:51:51

Increasing (with slope #5/9#)

#f(x) = (x^2-6x-12)/(x+2) = ((x^2+2x)-(8x+16)+4)/(x+2) = x-8+4/(x+2)#

So:

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

and:

#f'(1) = 1 - 4/(1+2)^2 = 1 - 4/9 = 5/9 > 0#

So #f(x)# is increasing at #x=1#

graph{(x^2-6x-12)/(x+2) [-8.59, 11.41, -7.28, 2.72]}