Velocity and turning
A cart's position is s(t)=t^3-6t^2+9t meters. Then v(t)=3t^2-12t+9=3(t-1)(t-3).
- Turning occurs when velocity changes sign.
- Critical times are t=1 and t=3.
- Check intervals, not zeros alone.
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LEARN MISSIONmotion, extrema, related rates, and optimization
motion, extrema, related rates, and optimization
When does the cart change direction for t>0?
MODELOptimization Console
CALC
PROVEChoose with evidence
CLUE
Pause. Find what matters. Then make your move.