1. The problem is to find the rate of change of a function without using integration. 2. Rate of change typically refers to the derivative of a function, which measures how the function's output changes as the input changes. 3. To solve this, identify the function $y=f(x)$ you want to analyze. 4. Compute the derivative $\frac{dy}{dx}$ using differentiation rules (power rule, product rule, quotient rule, chain rule, etc.) depending on the function. 5. The derivative $\frac{dy}{dx}$ represents the instantaneous rate of change of $y$ with respect to $x$. 6. Evaluate $\frac{dy}{dx}$ at specific points if needed to find the rate of change at those points. 7. No integration is involved; only differentiation is used to find the rate of change. This method applies to any differentiable function to find its rate of change.