What is the instantaneous rate of change of #f(x)=xe^(x^2-x) # at #x=3 #?

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Answer 1 · 2018-05-24T12:57:12

Instantaneous rate of change of #f(x)# at #x=3# is
# 6454.86# unit

#f(x)=x e^(x^2-x) ; x=3#

#f^'(x)= 1*e^(x^2-x)+ x *e^(x^2-x)(2 x-1)# or

#f^'(x)= e^(x^2-x)+ x(2 x-1) *e^(x^2-x)#

#f^'(3)= e^(3^2-3)+ 3(6-1) *e^(3^2-3)# or

#f^'(3)= e^6+15 *e^6# or

#f^'(3)= 16 *e^6 = 6454.86#

Instantaneous rate of change of #f(x)# is # 6454.86# unit [Ans]