Is #f(x)=(3x^3-2x^2-2x+5)/(x+2)# increasing or decreasing at #x=3#?

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Answer 1 · 2016-01-07T06:13:05

#f'(x) =6x - 8 + 23/(x+2)^2#
and
#f'(3) = 273/25=10+23/25=10.92#

increasing

given

#f(x)= (3x^3 - 2x^2 -2x +5)/(x+2)#

proceed by dividing

#3x^3 - 2x^2 -2x + 5# by #x+2#

to obtain

#f(x) = 3x^2 - 8x +14 -23/(x+2)#

find the first derivative to obtain

#f '(x) = 6x - 8+ 23/(x+2)^2#

evaluate

#f '(3) = 6(3)-8+23/(3+2)^2 = 10.92#

which indicates INCREASING at #x=3#