Question

How do you find the instantaneous rate of change of g with respect to x at x=2 if `g(x)=2x^2`?

Answer 1

Instantaneous Rate of Change = derivative `(dg(x))/dx=g'(x)`
In your case:

`g'(x)=4x`

at `x=2`

`g'(2)=4*2=8`