Is #f(x)=(x^2-6x-12)/(x+2)# increasing or decreasing at #x=1#?
1 Answer
Mar 13, 2016
Increasing (with slope
Explanation:
#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
graph{(x^2-6x-12)/(x+2) [-8.59, 11.41, -7.28, 2.72]}