Find the absolute maximum and absolute minimum values of the function, if they e
ID: 2831800 • Letter: F
Question
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) = 6x + 2; [-1, 2]
2.
f(x) = -21; [-7, 7]
3.
f(x) = x2 - 12x + 41; [ 2, 8]
4.
f(x) = x4 - 5x3; [-5, 5]
5.
f(x) = -3 - 7x; [-3, 1]
6.
f(x) = 4x2 - 5x3; [0, 5]
7.
8.
9.
10.
f(x) = x3 - 4x2 - 16x + 1; [-9, 0]
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) = 6x + 2; [-1, 2]
A) There are no absolute extrema.B) Absolute maximum: -1, absolute minimum: 2
C) Absolute maximum: 12, absolute minimum: -6
D) Absolute maximum: 14, absolute minimum: -4
2.
f(x) = -21; [-7, 7]
A) Absolute maximum: 21, absolute minimum: -21B) Absolute maximum: 21, absolute minimum: 0
C) Absolute maximum: -21, absolute minimum: -21
D) There are no absolute extrema.
3.
f(x) = x2 - 12x + 41; [ 2, 8]
A) Absolute maximum: 21, absolute minimum: 5B) Absolute maximum: 21, absolute minimum: 9
C) Absolute maximum: 9, absolute minimum: 5
D) Absolute maximum: 5
4.
f(x) = x4 - 5x3; [-5, 5]
A) Absolute maximum: 1250, absolute minimum: 0B) Absolute maximum: 625, absolute minimum: -
C) Absolute maximum: 0, absolute minimum: -
D) Absolute maximum: 1250, absolute minimum: -
5.
f(x) = -3 - 7x; [-3, 1]
A) Absolute maximum: 18, absolute minimum: -10B) Absolute maximum: -10, absolute minimum: -24
C) There are no absolute extrema
D) Absolute maximum: 24, absolute minimum: -4
6.
f(x) = 4x2 - 5x3; [0, 5]
A) Absolute maximum:, absolute minimum: 0B) Absolute maximum:, absolute minimum: 0
C) No absolute maximum, absolute minimum: -525
D) Absolute maximum:, absolute minimum: -525
7.
A)B) Absolute maximum: , absolute minimum: -5.33
C) Absolute maximum: 5.33, absolute minimum: -5.33
D) Absolute maximum: 5.33, absolute minimum:
8.
A) Absolute maximum: -8, absolute minimum: -15B) Absolute maximum: -8, absolute minimum: -
C) Absolute maximum: -, absolute minimum: - 17
D) Absolute maximum: 8, absolute minimum: - 17
9.
A) Absolute maximum: 6, absolute minimum: 2B) Absolute maximum: 2, absolute minimum: -
C) Absolute maximum: , absolute minimum -
D) Absolute maximum: 6, absolute minimum -
10.
f(x) = x3 - 4x2 - 16x + 1; [-9, 0]
A) Absolute maximum: , absolute minimum: 550B) There are no absolute extrema.
C) Absolute maximum: , absolute minimum: -908
D) Absolute maximum: -908 , absolute minimum: 16875 256
Explanation / Answer
1) D
2)C
3) A
4)D
5)A
6)D
7)B
8)D(there is a mistake of minus)
9)D
10)C
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