Seeing graphs can really help you understand differentiation in Year 9 Math. When you look at a function’s graph, the slope of a line that just touches it at any point shows its derivative. This connection helps you see how the function acts.

Why Visualization is Important:

1. Spotting Increasing and Decreasing Sections:

   • If the graph goes up, the function is increasing (we say $f'(x) > 0$).
   • If the graph goes down, the function is decreasing (we say $f'(x) < 0$).

2. Finding Highs and Lows:

   • Look for the highest and lowest points on the graph. At these spots, the derivative is zero (we say $f'(x) = 0$).

3. Understanding Curves:

   • If the graph curves up like a smile, it means the second derivative is positive (we say $f''(x) > 0$).
   • If it curves down like a frown, it means the second derivative is negative (we say $f''(x) < 0$).

When you draw graphs of functions, you can see these ideas clearly. This makes them easier to understand and use!