Question

How do you find the instantaneous rate of change for `f(x) = 3/x` for x=2?

Answer 1

Instantaneous rate of change for `f(x)=3/x` at `x=2`
is `-3/4`

Explanation:

`f(x)=3/x=3*x^(-1)`

The general instantaneous rate of change is given by the derivative:
`color(white)("XXX")(d f(x))/(dx) = -3*x^(-2) = -3/(x^2)`

At `x=2` this becomes
`color(white)("XXX")-3/(2^2) = -3/4`
graph{ (3/x-y) (3.0*x/4.0+y-3.0)=0 [-4.5,4.5,-2.2,2.7]}