Question: Estimate $\frac{f(2+h)-f(2)}{h}$ for $h = 1$.
1. **State the problem:** We need to estimate the difference quotient $$\frac{f(2+h)-f(2)}{h}$$ for $h=1$. This expression represents the average rate of change of the function $f(x)$ from $x=2$ to $x=2+1=3$.
2. **Formula used:** The difference quotient is given by $$\frac{f(2+h)-f(2)}{h}$$ where $h$ is the increment in $x$.
3. **Apply the values:** Substitute $h=1$:
$$\frac{f(2+1)-f(2)}{1} = f(3) - f(2)$$
4. **Estimate values from the graph:** From the description,
- $f(2) \approx 2.0$
- $f(3) \approx 3.1$
5. **Calculate the difference quotient:**
$$f(3) - f(2) = 3.1 - 2.0 = 1.1$$
6. **Final answer:**
$$\frac{f(2+1)-f(2)}{1} = 1.1$$
This means the average rate of change of $f(x)$ from $x=2$ to $x=3$ is approximately $1.1$.