Question

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

Answer 1

-3/4 is the instantaneous rate of change at x=2.

Explanation:

Instantaneous rate of change can be found by finding the derivative of the equation. The equation in this particular problem can be rewritten as follows:

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

From here we can follow the power rule of derivatives and get the derivative function.

`f'(x) = -3(x^-2)`
or
`f'(x) = -3/x^2`

From here we can plug in our given, x=2, and get the answer.

`f'(2) = -3/4`