Maxima, Minima and Applications of Derivatives Short Notes for GATE DA: Concepts, Formulas, Worked Examples & Practice

Maxima, Minima and Applications of Derivatives short notes for GATE DA: 2 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

Quick Revision Cheat Sheet

Essential Checklist

Critical Point	$f^{'} (c) = 0$ or undefined
Local Min	$f^{'} (c) = 0$ AND $f^{''} (c) > 0$ ( $\cup$ )
Local Max	$f^{'} (c) = 0$ AND $f^{''} (c) < 0$ ( $\cap$ )
Test Fails	$f^{''} (c) = 0$ $\to$ Use First Derivative Test

Final Tip: Always verify if the function is differentiable at the critical point before applying the test.

The Extrema Checklist

Summary

The Extrema Checklist

Check Degree: Even = global extrema possible on $R$ ; Odd = none.
Differentiate: Find $f^{'} (x)$ and solve $f^{'} (x) = 0$ .
Filter: Keep only critical points $c$ with $a < c < b$ .
Evaluate $f$ at valid critical points + all included endpoints.
Compare: Highest = abs max; lowest = abs min.
Verify Attainment: Open/half-open? Ensure the extreme is reached, not just approached.

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Maxima, Minima and Applications of Derivatives Short Notes for GATE DA: Concepts, Formulas, Worked Examples & Practice

Maxima, Minima and Applications of Derivatives short notes for GATE DA: 2 study cards covering concepts, formulas, shortcuts and exam traps, plus solved pract

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