Sample Questions

Calculus I

Minima and Maxima

a) X = 0.5 and X = 1.5.

b) X = -0.5 and X = -1.5.

c) X = 0.5 and X = -1.5.

d) X = -0.5 and X = 1.5.

e) None of the above.

a) X = -0.5: minimum; X = -1.5: maximum.

b) X = -0.5: minimum; X = -1.5: minimum.

c) X = -0.5: maximum; X = -1.5: maximum.

d) X = -0.5: maximum; X = -1.5: minimum.

a) X = 1.0.

b) X = -1.0.

c) X = 0.

d) X = -2.0.

a) minimum.

b) maximum.

c) optimum.

d) point of inflection.

a) P = (5.5, 2.0).

b) P = (2.5, 5.0).

c) P = (5.0, 2.5).

d) P = (-5.0, -2.5).

a) f''(X) = 0.

b) f''(X) = -1.0.

c) f''(X) = 1.0.

d) f''(X) = -12.5.

a) P = (3.67, 40.11).

b) P = (6.33, 40.11).

c) P = (3.67, 6.33).

d) P = (-3.67, 40.11).

a) f''(X) = 6 * X - 40.

b) f''(X) = -18.0.

c) f''(X) = 18.0.

d) f''(X) = -22.0.

a) f(X) = 16 - X.

b) f(X) = 8 - X.

c) f(X) = 16 - 2 * X.

d) f(X) = 16 + 2 * X.

a) f''(X) = 16.0.

b) f''(X) = -16.0.

c) f''(X) = -8.0.

d) f''(X) = 32 / m.

a) f(X) = 12 - 0.75 * X.

b) f(X) = -12 + 0.75 * X.

c) f(X) = -12 - 0.75 * X.

d) f(X) = 12 + 0.75 * X.

a) f''(X) = 48.0.

b) f''(X) = -0.75.

c) f''(X) = 36.0.

d) f''(X) = 85.3.

a) 11.34 km under land and 17.32 km under water.

b) 17.32 km under land and 11.34 km under water.

c) 20.0 km under land and 15.0 km under water.

d) 8.66 km under land and 18.80 km under water.

a) f''(X) = -8.66.

b) f''(X) = 11.55.

c) f''(X) = 8.66.

d) f''(X) = -2.88.

a) Width = 300 m and Length = 300 m.

b) Width = 120 m and Length = 600 m.

c) Width = 300 m and Length = 150 m.

d) Width = 150 m and Length = 300 m.

a) f''(X) = -4 * W.

b) f''(X) = 4.0.

c) f''(X) = -4.0.

d) f''(X) = -2.0.

a) Equilateral of side length 30 cm.

b) Equilateral of side length 10 cm.

c) Isosceles of side length 12 cm and base length 6 cm.

d) A triangle of side lenths 8 cm, 10 cm, and 12 cm.

a) f'(9) = 3.35 and f'(11) = -2.20 therefore maximum.

b) f'(9) = -2.20 and f'(11) = 3.35 therefore maximum.

c) f'(9) = 3.35 and f'(11) = -2.20 therefore minimum.

d) f'(9) = 7.70 and f'(11) = -3.30 therefore maximum.

a) P = (3.0, 2.45).

b) P = (6.0, 18.0).

c) P = (1.22, 0.75).

d) P = (2.45, 3.0).

a) f'(√5) = -0.415 and f'(√7) = 0.491 therefore minimum.

b) f'(√5) = -0.415 and f'(√7) = 0.491 therefore maximum.

c) f'(√5) = 0.415 and f'(√7) = -0.491 therefore minimum.

d) f'(√5) = -0.491 and f'(√7) = 0.415 therefore maximum.

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