G11 SUPER GIO
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PRACTICE MISSIONmotion, extrema, related rates, and optimization

motion, extrema, related rates, and optimization

NEW CASENEW EVIDENCE

Optimize an open-top box

Cut squares of side x from a 20 cm by 12 cm sheet. Volume V(x)=x(20-2x)(12-2x), with 0<x<6. Solving V'(x)=12x^2-128x+240=0 gives critical points x about 2.43 and x about 8.24.

  1. Respect the physical domain.
  2. Only one critical point is feasible.
  3. Endpoints give zero volume.

Which cut gives the maximum feasible volume?

MODELOptimization Console
CALC
PROVEChoose with evidence
CLUE

Pause. Find what matters. Then make your move.