1. The derivative f'(x) starts as a positive constant (slope of the line), then decreases linearly to zero at the peak, and becomes negative with increasing magnitude (steepening slope down).
2. The derivative f'(x) starts negative, increases to zero at the first peak, becomes negative again at the valley, then positive at the second peak, and finally negative again.
3. The function f(x) starts flat (horizontal tangent), then increases slowly, accelerates to a steeper increase, then slows down to a horizontal tangent again.
4. The function f(x) starts with a steep negative slope, becomes less steep, crosses the x-axis with a horizontal tangent, then has a positive slope that increases linearly.
Parent Tip: Review the logic above to help your child master the concept of derivatives from graphs worksheet.
