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64
A square 8×8 maximises this model.
Class 12 · English Version · Mathematics
Equations, patterns and functions
Solve optimisation and area problems with boundaries checked.
About this lesson and its coverage
Original Kidemy Class 12 progression. This level has its own text, examples and questions. Curriculum versions share the progression; complete board-specific coverage still needs specification matching and additional material.
Learn the idea
Stationary points are candidates, not automatic maxima. A constrained problem needs its domain, stationary values and relevant boundaries checked. For area between curves, integrate upper minus lower on intervals where their order is known.
Worked example
For a rectangle with perimeter 24, A=x(12−x)=36−(x−6)²,0<x<12. Maximum area 36 occurs at x=6.
- Identify the quantities and restrictions.
- Show a method with units or symbols.
- Check and explain the result.
Your written practice
Show your working on paper. Check your answer, then choose Next.
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26
[x³]1 to 3=27−1.
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0.5
d/dx ln x=1/x for x>0.
Write in your own words. A guardian or teacher should review this response.
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∫(x−x²)dx=[x²/2−x³/3]0 to 1=1/6.
Identify upper and lower curves.
Write in your own words. A guardian or teacher should review this response.
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The largest or smallest value can occur at an endpoint even without zero derivative there.
Explain candidate comparison.
Progress and browser storage
Notebook challenge, sources and further study
Apply the idea
Write a constrained optimisation solution including domain and boundary reasoning.
Review with a guardian or teacher
- Use the stated evidence or givens.
- Show reasoning rather than only a result.
- Review and explain one correction.
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