Determine the absolute extrema of the function f(x)=(x-3)e^x on the interval

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Given function isf(x)=(x-3)e^(x)quad,-1 <= x <= 3Differentiating with respect to ' x ', we have{:[f^(')(x)=(x-3)e^(x)+1xxe^(x)],[" or, "f^(')(x)=(x-2)e^(x)]:}For eritical points, we have{:[f^(')(x)=0],[=>(x-2)e^(x)=0],[=>x-2=0quad[:'e^(x)!=0" in "-1 <= x <= 3]],[=>x=2.]:}:. The critical point of the function f(x) is x=2To kind the aboulute extr ... See the full answer