What should we choose when the derivative solution lies outside the feasible range?
List the feasible set first, then compare every stationary point and boundary.
Follow the cause and effect
Write the objective together with its feasible interval.
Find the first derivative and inspect its sign or curvature.
Evaluate every candidate and choose the feasible maximum.
The model you are using
Conditions for this model
Output is continuous and nonnegative; the cost function includes economic costs.
The exam trap
Do not stop at the FOC; it may be a minimum, infeasible, or absent.
Connect the reasoning to the graph
What changes
- A profit-versus-q graph shows the highest feasible value, not merely where slope is zero.
What stays fixed
Output is continuous and nonnegative; the cost function includes economic costs.
Keep these conditions throughout the comparison; change only what the case above specifies.
What to inspect
Evaluate every candidate and choose the feasible maximum.
Compare before and after, and locate the conclusion on the graph.
5 MINUTES · TRANSFER THE IDEA
Can you explain it without the lesson?
Solve π(q)=18q−q²−20 for 0≤q≤6 and justify the chosen quantity.