Let's solve this graphically by estimating the slopes of the tangent lines to the curve at the points $x = 0$ and $x = 1$, which represent $f'(0)$ and $f'(1)$.

$f'(0)$ (Slope at $x = 0$):

Looking at the graph around $x = 0$, the curve is increasing. The slope appears positive but not steep. It looks like the rise is about 2 units for a run of 1 unit, so the slope is approximately: $f'(0) \approx 2.$

$f'(1)$ (Slope at $x = 1$):

At $x = 1$, the graph flattens out, indicating that the slope here is very close to 0. Therefore: $f'(1) \approx 0.$

Thus, the estimates are: $f'(0) \approx 2, \quad f'(1) \approx 0.$

Would you like a more detailed explanation of how the slopes are calculated, or do you have any questions? Here are some follow-up questions that could help deepen your understanding:

1. What does the slope of a tangent line represent in terms of the function's behavior?
2. How can you tell whether a function is increasing or decreasing from its derivative?
3. What would the second derivative tell you about the concavity of the graph?
4. Why is the slope zero at certain points (like at $f'(1)$)?
5. How can you graphically interpret inflection points using the second derivative?

Tip: When interpreting slopes from a graph, the tangent line's angle gives an approximation of how steeply the function is increasing or decreasing.