Extremwertaufgaben

    1. x = y = 6
    2. x = y = 6
    3. x = 8, y = 4
    4. x = 9, y = 3

    1. a = b = u/4 (25 cm), A = u²/16 (625 cm²)
    2. a = b = d/√2 (70,7 cm), A = d²/2 (0,5 m²)

    1. a = b = √A (10 cm), u = 4√A (40 cm)
    2. a = b = √A (10 cm), d = √(2A) (14,1 cm)

    1. x = 5 cm, V = 2250 cm³
    2. x = 10 cm, V = 16000 cm³

  5. b = d/√3 (43,3 cm), h = d√2/√3 (61,2 cm)

  6. x = y = 60 cm, z = 30 cm, V = 108 dm³

  7. a = h = ³√V (10 cm) - Würfel

  8. r = ³√(V/2π) (5 cm), h = 2·³√(V/2π) (10 cm)

  9. r = h = ³√(V/π) (6,3 cm)

  10. x = 5 cm, y = 8 cm, z = 20 cm, O = 600 cm²

    1. x = a/2 (15 cm), y = b/2 (20 cm), A = ab/4 (300 cm²)
    2. x = c/2 (25 cm), b = hc/2 (12 cm), A = c·hc/4 (300 cm²)

    1. r = R/√2 (8,5 cm), h = R√2 (17,0 cm)
    2. r = R√8/3 (11,3 cm), h = 4R/3 (16 cm)

    1. r = R√2/√3 (9,8 cm), h = R/√3 (6,9 cm)
    2. r = R, h = 0 (Randextremum)

    1. keine Lösung
    2. r = 50 cm, h = 1 cm (Randextremum)

  15. x = y = u/3 (33,3 cm), A = u²√3/36 (481 cm²)

  16. x = π/(4+π) m = 44 cm, y = 4/(4+π) m = 56 cm

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