Find the absolute maximum and absolute minimum values of the function, if they exist, over the indicated interval.
When no interval is specified, use the real line (-∞, ∞).
1.
f(x) = 4x2 - 5x3; [0, 5]
A) Absolute maximum:
, absolute minimum: 0
B) Absolute maximum:
, absolute minimum: -525
C) No absolute maximum, absolute minimum: -525
D) Absolute maximum:
, absolute minimum: 0
2.
f(x) = -21; [-7, 7]
A) Absolute maximum: 21, absolute minimum: 0
B) Absolute maximum: -21, absolute minimum: -21
C) There are no absolute extrema.
D) Absolute maximum: 21, absolute minimum: -21
3.
f(x) = x3 - 4x2 - 16x + 1; [-9, 0]
A) There are no absolute extrema.
B) Absolute maximum:
, absolute minimum: 550
C) Absolute maximum: -908 , absolute minimum:
D) Absolute maximum:
, absolute minimum: -908
4.
f(x) = x4 - 5x3; [-5, 5]
A) Absolute maximum: 1250, absolute minimum: B) Absolute maximum: 625, absolute minimum: C) Absolute maximum: 0, absolute minimum: 5.
D) Absolute maximum: 1250, absolute minimum: 0
A)
B) Absolute maximum: 5.33, absolute minimum: -5.33
C) Absolute maximum:
, absolute minimum: -5.33
D) Absolute maximum: 5.33, absolute minimum:
6.
f(x) = x2 - 12x + 41; [ 2, 8]
A) Absolute maximum: 9, absolute minimum: 5
B) Absolute maximum: 21, absolute minimum: 5
C) Absolute maximum: 5
D) Absolute maximum: 21, absolute minimum: 9
7.
f(x) = -3 - 7x; [-3, 1]
A) Absolute maximum: -10, absolute minimum: -24
B) Absolute maximum: 18, absolute minimum: -10
C) Absolute maximum: 24, absolute minimum: -4
D) There are no absolute extrema
8.
A) Absolute maximum: 8, absolute minimum: - 17
B) Absolute maximum: -8, absolute minimum: -15
C) Absolute maximum: -8, absolute minimum: -
9.
D) Absolute maximum: -
, absolute minimum: - 17
A) Absolute maximum: 6, absolute minimum: 2
B) Absolute maximum: 2, absolute minimum: C) Absolute maximum: 6, absolute minimum D) Absolute maximum:
10.
f(x) = 6x + 2; [-1, 2]
, absolute minimum -
A) Absolute maximum: 12, absolute minimum: -6
B) Absolute maximum: 14, absolute minimum: -4
C) Absolute maximum: -1, absolute minimum: 2
D) There are no absolute extrema.
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