1. **State the problem:** Optimization involves finding the maximum or minimum value of a function, often subject to certain constraints. 2. **Identify the function to optimize:** This is usually called the objective function, denoted as $f(x)$ or $f(x,y)$ for one or two variables. 3. **Find the derivative(s):** Compute the first derivative $f'(x)$ for one variable or partial derivatives $\frac{\partial f}{\partial x}$ and $\frac{\partial f}{\partial y}$ for two variables. 4. **Set the derivative(s) equal to zero:** Solve $f'(x) = 0$ or $\frac{\partial f}{\partial x} = 0$, $\frac{\partial f}{\partial y} = 0$ to find critical points. 5. **Check the critical points:** Use the second derivative test or the Hessian matrix to determine if each critical point is a maximum, minimum, or saddle point. 6. **Evaluate endpoints or constraints:** If the domain is restricted, evaluate the function at the boundaries or use methods like Lagrange multipliers for constrained optimization. 7. **Choose the optimal value:** Compare all candidates from critical points and boundaries to find the absolute maximum or minimum. This process helps you systematically find the best solution to optimization problems.