Is #f(x)=(4x^3+5x^2-2x+7)/(x+1)# increasing or decreasing at #x=0#?

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Answer 1 · 2016-01-12T08:51:07

Decreasing at x=0

Get the first derivative of f(x)

#f(x)=(4x^3+5x^2-2x+7)#

#f' (x) =((x+1)*(12x^2+10x-2)-(4x^3+5x^2-2x+7)(1))/(x+1)^2#

substitute #x=0#

#f' (0) =((0+1)*(12(0)^2+10(0)-2)-(4(0)^3+5(0)^2-2(0)+7)(1))/(0+1)^2#

#f' (0) =((0+1)(-2)-7)/1^2#

#f' (0)= -9# negative means decreasing at x=0