Answer:
-1/36
Step-by-step explanation:
Estimate the instantaneous rate of change at the point indicated
To find the instantaneous rate of change we find the derivative of the given function
Instantaneous rate of change is the rate of change at the given point
[tex]f(x)=\frac{1}{x+2}[/tex]
To find derivative we apply power rule
[tex]f(x)=(x+2)^{-1}[/tex]
[tex]f'(x)=-1(x+2)^{-2}[/tex]
[tex]f'(x)=\frac{-1}{(x+2)^2}[/tex]
Now plug in 4 for x in f'(x)
[tex]f'(4)=\frac{-1}{(4+2)^2}[/tex]
[tex]f'(4)=\frac{-1}{36}[/tex]
