Application of Derivatives Class 12 Maths Notes – Formulas & Quick Revision

Application of Derivatives mein rate of change, increasing-decreasing, tangent-normal aur maxima-minima aate hain. Yahan aapko is chapter ke sabse important formulas aur quick revision points free milte hain — NCERT/CBSE syllabus ke hisaab se, boards aur JEE/NEET dono ke liye.

Important Formulas & Concepts — Application of Derivatives

• Rate: dy/dt = (dy/dx)(dx/dt)
• Increasing: f′(x) > 0; decreasing: f′(x) < 0
• Tangent slope = f′(x₀); normal slope = −1/f′(x₀)
• Critical points: f′(x) = 0
• Second derivative test: f″ > 0 minima, f″ < 0 maxima
• Absolute max/min: critical points + endpoints check karo
• Word problems: area/volume ko single variable mein express karo
• Marginal cost/revenue = derivative

Quick Revision Points

• Maxima-minima ka 6-marker word problem boards mein pakka hai
• Closed interval mein endpoints check karna mat bhoolo
• Increasing/decreasing intervals mein critical points se number line banao
• Cylinder/cone/sphere ke standard results yaad rakho
• Constraint ko use karke ek variable eliminate karo

FAQ

Word problems kahan se shuru karun?

Diagram banao → variables → constraint → single variable function → differentiate. PDF mein ye 5-step format solved hai.

Rationalised syllabus mein kya hata?

Approximations hat gaye — maxima/minima aur monotonicity par focus karo.

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