The expression $f(a+h)$ represents the value of a function $f(x)$ at the point $x = a + h$, where $a$ is a specific point on the curve, and $h$ is a small increment (or change) from that point.

In the context of curves, particularly when talking about calculus and derivatives:

1. At $x = a + h$: The point on the curve is determined by the value of the function at $a + h$, which means $f(a+h)$ gives the height or $y$-value of the curve at that $x$-coordinate.

2. When $h$ is small: If you're dealing with limits and derivatives, $f(a+h)$ is used to explore the behavior of the function as you move slightly away from $a$. For instance, when finding the derivative, you compute how much the function changes between $f(a)$ and $f(a+h)$ as $h \to 0$.

This is essential for calculating the slope of the tangent line at a point $a$, using the formula for the derivative:

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

Would you like more details or clarification on this?

Here are some related questions you might find helpful:

1. What is the geometric meaning of the derivative at a point?
2. How does $f(a+h)$ relate to the concept of a difference quotient?
3. How do you calculate the slope of a curve using $f(a+h)$?
4. What happens to $f(a+h)$ as $h \to 0$?
5. How is $f(a+h)$ used in Taylor series expansions?

Tip: In calculus, $f(a+h)$ is fundamental in understanding changes in the function near $x = a$, leading to key concepts like limits, slopes, and concavity.