1. The problem is to find the slope of a curve or the rate of change of a function without using differentiation. 2. One common method is to use the definition of the derivative as a limit of the difference quotient: $$m = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$$ 3. This means we calculate the average rate of change over a very small interval $h$ and then let $h$ approach zero. 4. For example, if $f(x) = x^2$, then: $$\frac{f(x+h) - f(x)}{h} = \frac{(x+h)^2 - x^2}{h} = \frac{x^2 + 2xh + h^2 - x^2}{h} = \frac{2xh + h^2}{h} = 2x + h$$ 5. Taking the limit as $h \to 0$ gives: $$m = 2x$$ 6. This matches the derivative but was found without directly differentiating, just using the limit definition. 7. This method can be applied to any function where the limit exists to find the slope at a point without using differentiation rules.