Calc A

Matching Functions with its dervitive

The 3 Core Rules

1. Peaks & Valleys $\rightarrow$ Zero Hits

   • Wherever f(x) has a top peak or a bottom valley, f'(x) must cross the x-axis (touch zero) at that exact same spot.

2. Going Up vs. Going Down

   • If f(x) is climbing upward (left to right), $f'(x)$ is above the x-axis (positive).

   • If f(x) is sliding downward (left to right), $f'(x)$ is below the x-axis (negative).

3. Straight Lines $\rightarrow$ Flat Lines

   • If $f(x)$ has straight slanted lines, its slope doesn't change, so $f'(x)$ will be flat horizontal lines.