Question

What is the instantaneous rate of change of `f(x)=(x-5)^2` at `x=2`?

Answer 1

The instantaneous rate of change of `f(x)` at `x=2` is `-6`.

Explanation:

Rate of change of `f(x)=(x-5)^2` is given by `(df)/dx`, which is given by

`(df)/dx=2*(x-5)=2x-10`.

As at `x=2`, `(df)/dx=2xx2-10=-6`,

the instantaneous rate of change of `f(x)` at `x=2` is `-6`.