Question

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

Answer 1

Have you learned differentiation formulas yet, or do you need to do this using the definition?

Using differentiation formulas, find `f"(x)` and the evaluate at `x=2`

`f'(x)=2x+3`,

so the instantaneous rate of change when `x=2` is `f'(2)=2(2)+3=7`