What are the extrema of #f(x) = e^x(x^2+2x+1)#?

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Answer 1 · 2016-04-05T21:18:21

x=-3 or x = -1

#f=e^x, g=x^2+2x+1#

#f'=e^x, g'=2x+2#

#f'(x)=fg'+gf'=e^x (2x+2)+e^x (x^2+2x+1)=0#

#e^x (2x+2+x^2+2x+1)=0#

#e^x (x^2+4x+3)=0#

#e^x(x+3)(x+1)=0#

#e^x = 0 or x+3=0 or x+1 =0#

not possible, #x=-3 or x = -1#

#f(-3)=e^-3(9-6+1)=0.199#->max

#f(-1)=e^-1(1-2+1) = 0#->min