Question

How do you find the instantaneous rate of change of `f(x)=4x^2+4x−3` when `x=4`?

Answer 1

The instantaneous rate of change is equal to the slope of the tangent at the required point or, equivalently, the derivative of the function evaluated at that point.

If `f(x) = 4x^2 + 4x -3`
then
the derivative is `f'(x) = 8x + 4`

Evaluating this derivative at `x=4`
gives the instantaneous rate of change
`8(4)+4 = 36`