What is the instantaneous rate of change of #f(x)=x-e^(x^2-7) # at #x=3 #?

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Answer 1 · 2016-06-04T03:02:24

#f' (3)=1-6*e^(2)#
#f' (3)=-43.33433659#

Instantaneous rate of change is the first derivative #f' (x)#

From the given #f(x)=x-e^(x^2-7)#

The first derivative is

#f(x)=x-e^(x^2-7)#

#f' (x)=1-e^(x^2-7)*d/dx(x^2-7)#

#f' (x)=1-e^(x^2-7)*(2x-0)#

#f' (x)=1-2x*e^(x^2-7)#

at #x=3#

#f' (3)=1-2*(3)*e^(3^2-7)#

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

God bless...I hope the explanation is useful.