g10-03-04 · Core topics
A profitable value may be impossible
Which non-loss solutions are feasible in the context?
1 MIN · PREDICT ON PAPER
Predict the feasible set for P(x)=a(x−r)(x−s)≥0 under 0≤x≤d, then require integer x.
Discuss or write first. No typed answer is required to continue.
Solution: [2, 8]
2 MIN · EXPLAIN AND REVISE
Which condition does your claim need?
Compare at least two cases. Write a reason, then check the explanation together.
Reveal explanation and conditions
The final choice is the intersection of the sign solution, the contextual interval and, when required, the integers. Finite displayed cases suggest a conjecture; the justification below states why it holds under the stated conditions.
Conditions: The profit expression is a mathematical scenario; d≥1 and the integer restriction is explicit.
Mathematical justification: An x is acceptable iff it satisfies every constraint. Solving the polynomial first and intersecting cannot add an input failing any original condition.
1 MIN · EXIT CHECK
P(x)=−(x−2)(x−8), 0≤x≤6. Find feasible integer non-loss sizes.
Check after answering
2,3,4,5,6. The contextual upper bound removes 7 and 8.
Teacher guidance and extension
Before: Polynomial signs and intersections
Ask: Ask students to circle which restriction removes each rejected candidate.
Watch for: A real root outside the contextual domain is not a feasible activity size.
Challenge: Find parameters with real feasible values but no feasible integer.
Suggested timing: predict 1 min, compare 3 min, explain 2 min, exit check 1 min. Observations can suggest a claim; they do not prove it for every input.
Optional local notebook
Paper responses are enough. Drafts remain in this tab; choose local saving to include them in the existing complete backup.
Complete backup and restore