# What is the instantaneous rate of change of #f(x)=1/(x-7 )# at #x=0 #?

##### 1 Answer

Aug 1, 2016

#### Explanation:

The

#color(blue)"instantaneous rate of change"# derives from the value of f'(0).

#f(x)=1/(x-7)=(x-7)^-1#

#rArrf'(x)=-1(x-7)^-2.d/dx(x-7)=-(x-7)^-2 .1=-1/(x-7)^2# and

#f'(0)=-1/(0-7)^2=-1/49#