1. **State the problem:** We are given a function $g(x)$ and asked to find its derivative $g'(x)$ and then solve for $x$ when $g'(x) = 4$. 2. **Find $g'(x)$:** Since the function $g(x)$ is not explicitly given, we assume it is known or provided elsewhere. The derivative $g'(x)$ is found by applying the rules of differentiation to $g(x)$. 3. **Set $g'(x) = 4$ and solve for $x$:** Once $g'(x)$ is found, we solve the equation $g'(x) = 4$ to find the value(s) of $x$. 4. **Example:** If $g(x) = x^2 + 3x + 2$, then $$g'(x) = \frac{d}{dx}(x^2 + 3x + 2) = 2x + 3.$$ Set $g'(x) = 4$: $$2x + 3 = 4.$$ Subtract 3 from both sides: $$2x + \cancel{3} - \cancel{3} = 4 - 3,$$ $$2x = 1.$$ Divide both sides by 2: $$\frac{\cancel{2}x}{\cancel{2}} = \frac{1}{2},$$ $$x = \frac{1}{2}.$$ **Final answers:** (i) $g'(x) = 2x + 3$ (ii) $x = \frac{1}{2}$