Question

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

Answer 1

Take the derivative of `f(x)` and evaluate it at `x=2` to get `-3/4`.

Explanation:

Instantaneous rate of change is simply the derivative of a function at a point. So begin by finding the derivative of `f(x)` using the power rule:
`f(x)=3/x=3x^(-1)`
`f'(x)=-1*3^(-1-1)=-3x^(-2)`

Now we evaluate it at `x=2` to find instantaneous rate of change:
`f'(x)=-3x^(-2)`
`f'(2)=-3(2)^(-2)=-3(1/4)=-3/4`

Therefore the instantaneous rate of change of `f(x)=3/x` at `x=2` is `-3/4`.