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Second Derivative Test in AP Calculus: A Critical Analysis

Learn the Second Derivative Test in calculus to determine relative maxima and minima. Interpret results based on f’’(c) values. Practice sketching and identifying critical points.

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Second Derivative Test in AP Calculus: A Critical Analysis

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  1. AP Calculus AB Day 6 Section 3.4 Perkins

  2. Second Derivative Test If c is a critical number of f’(x) and… (c, f(c)) is a relative min If f’’(c) > 0 then ______________________________________________ (c, f(c)) is a relative max If f’’(c) < 0 then _______________________________________________ the test fails (use 1st Derivative test) If f’’(c) = 0 or is undefined then __________________________________

  3. Crit numbers: 1. Find the extrema of 2nd Derivative Test rel max at rel min at rel max at rel min at

  4. Crit numbers: 2. Sketch 2nd Derivative Test rel max at rel min at Crit numbers: Intervals: Test values: f ’’(test pt) f(x) Inf pt

  5. 2 2 -2

  6. AP Calculus AB Day 6 Section 3.4 Perkins

  7. Second Derivative Test If c is a critical number of f’(x) and… If f’’(c) > 0 then ______________________________________________ If f’’(c) < 0 then _______________________________________________ If f’’(c) = 0 or is undefined then __________________________________

  8. 1. Find the extrema of

  9. 2. Sketch

  10. 2 2 -2

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