The image depicts the definition of the derivative of a function $f(x)$. It is given as:

$f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}$

This formula is the foundation of differential calculus and is used to calculate the derivative of a function $f(x)$ at a specific point $x$. It represents the slope of the tangent line to the graph of $f(x)$ at that point.

Would you like me to demonstrate an example using this formula, explain its meaning in more detail, or explore a specific application?

Relative Questions:

1. What does the derivative physically represent in real-world problems?
2. How can this formula be applied to find the derivative of $f(x) = x^2$?
3. Why does the limit $h \to 0$ ensure accuracy in calculating the slope?
4. What is the geometric interpretation of $f'(x)$?
5. How is this formula related to instantaneous rates of change?

Tip:

When solving for a derivative using this formula, simplify the numerator $f(x+h) - f(x)$ as much as possible before dividing by $h$.