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12
3x²=12.
Class 11 · Bangla Version · Mathematics
Equations, patterns and functions
Differentiate polynomials and use a definite integral as accumulation.
About this lesson and its coverage
Original Kidemy Class 11 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
A derivative gives local rate of change. Stationary points have zero derivative but need classification. A definite integral gives signed accumulation; area between a curve and axis may require splitting at roots.
Worked example
For y=x³−6x, y′=3x²−6. For y=3x², the integral of 3x² from 0 to 2 is [x³] from 0 to 2 = 8. Units of an integral combine the horizontal and vertical units.
- 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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16
[x²]0 to 4=16.
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5
2x−10=0.
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y″=2>0, so it is a local minimum at x=5.
Use curvature or derivative sign changes.
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The negative and positive signed parts cancel; areas counted positively are 1/2+1/2.
Distinguish signed accumulation from area.
Progress and browser storage
Notebook challenge, sources and further study
Apply the idea
Analyse a polynomial’s derivative and integral using a labelled sketch.
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- Use the stated evidence or givens.
- Show reasoning rather than only a result.
- Review and explain one correction.
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