TEST BANK FOR CALCULUS AND ITS APPLICATIONS (QUESTIONS WITH CORRECT ANSWERS)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the relative extrema of the function, if they exist.
1) f(x) = x2 - 8x + 18
A) Relative minimum at (4,2)
B) Relative maximum at (2, 4)
C) Relative maximum at (4, 2)
D) Relative minimum at (2, 4)
Answer: A

2) f(x) = 2x2 + 20x + 53
A) Relative minimum at (-5,3)
B) Relative maximum at (5,-3)
C) Relative minimum at (-3,5)
D) Relative minimum at (3,-5)
Answer: A

3) s(x) = -x2 - 12x - 27
A) Relative maximum at (-12,-27)
B) Relative maximum at (-6, 9)
C) Relative maximum at (6, 9)
D) Relative minimum at (12,-27)
Answer: B

4) f(x) = -7x2 - 2x - 2
1 13
A) Relative minimum at ,
7 7
1 13
B) Relative maximumiat - , -
7 7
13
C) Relative maximumat -7, -
7
D) Relative maximumiat 1 , 13
77
Answer: B

5) f(x) = 0.4x2 - 2.9x + 5.8
A) Relativeminimumat (3.625,0.54375)
B) Relativemaximum at(3.625,0.54375)
C) Relative minimum at (-3.625,21.56875)
D) Relative minimumat(3.625, 0)
Answer: A

6) f(x) = x3 - 3x2 + 1
A) Relative maximum at (-2, -19); relative maximum at (0,1)
B) Relative maximum at (0, 1); relative minimum at (2,-3)
C) Relative maximum at (2, -3)
D) Relative minimum at (0, 1); relative maximum at (2, -3)
Answer: B




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, 7) y = x3 - 3x2 + 7x - 10
A) Relative maximum at (2, 6)
B) Relative minimum at (1, 6)
C) Relative maximum at (-1, 6)
D) No relative extrema exist
Answer: D

8) f(x) = x3 - 12x + 4
A) Relative maximum at (5, 69); relative minimum at (-3,13)
B) Relative maximum at (5, 69); relative minimum at (2,-12)
C) Relative minimum at (-2, 20); relative maximum at (2,-12)
D) Relative maximum at (-2, 20); relative minimum at (2, -12)
Answer: D

9) f(x) = -4x3 + 4
A) Relative maximum at (0, -4)
B) Relative maximum at (0, 4)
C) Relative minimum at (0, 4)
D) No relative extrema exist
Answer: D

2 3 1 2
10) f(x) = x + x - 21x + 2
3 2
7 1273
A) Relative maximumat - , ; relative minimum 7 , - 883
at
2 24 2 24
77
3, -
B) Relative maximumat
2
7 1273 i ; relative minimum at 3, - 77
C) Relative maximumat - ,
2 24 2
103
D) Relative maximum at -3, ; irelative minimumat 7,- 883
2 2 24
Answer: C

11) f(x) = 3x4 + 16x3 + 24x2 + 32
A) Relative minimum at (-2, 48), relative maximum at (0,32)
B) Relative minimum at (0, 32)
C) Relative maximum at (-2, 48), relative minimum at (0,32)
D) Relative minimum at (-2,48)
Answer: B

12) f(x) = x4 -8x2 + 6
A) Relative maximum at (2, -10); relative minimum at (-2,-10)
B) Relative minimum at (0, 6); relative maxima at (2, -10), (-2, -22)
C) Relative maximum at (0, 6);relative minimum at (2, -10)
D) Relative maximum at (0, 6); relative minima at (2,-10), (-2, -
10) Answer: D




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,13) f(x) = x3 - 5x4
3 27
A) Relative maximum at (0,0); relative minima at - , - and 3 , 27
20 6400 20 32000
i3 27
B) Relative maximum at ,
20 32000
3 27
C) Relative maximumat , ; relative minimum at (0, 0)
20 32000
3 27
D) Relative minimum at - , - ; relative maximum at (0, 0)
20 6400
Answer: B

x2 + 1
14) f(x)
= x2

A) No relative extrema exist
B) Relative maximum at (-1, 2); relative minimum at (1,2)
C) Relative maximum at (0, 1)
D) Relative minimum at (0, 1)
Answer: A
4
15) f(x) =
x2 -1
A) No relative extrema exist
B) Relative minimum at (0, -4)
C) Relative maximum at (0, 4)
D) Relative maximum at (0,-4)
Answer: D

-6
16) f(x)
2
x +1
=
A) Relative maximum at (0, -6)
B) Relative minimum at (0, -6)
C) Relative maximum at (0, 6)
D) No relative extrema exist
Answer: B
6x
17) f(x) =
x2 + 1
A) Relative minimum at -1, - 3 ; relative maximum at 1, 3
B) Relative maximum at (0, 0)
C) Relative minimum at -1, - 3 ; relative maximum at (0, 0)
D) Relativemaximumat -1, -3 ; relativeminimum at 1, 3
Answer: A




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, x +1
18) f(x) =
x2 + 3x + 3
1
A) Relativemaximumat 0, ; relativeminimum at -2, -1
3
1 1
B) Relative minimum at 0, ; relative maximum at -2,
3 3
C) No relative extrema exist
1
-2,
D) Relative maximum at (0, 3); relative minimum at
3
Answer: A

19) f(x) = x2/5 - 1
A) Relative minimum at (0, -1); relative maximum at (1,0)
B) No relative extrema exist
C) Relative maximum at (0, -1)
D) Relative minimum at (0,-1)
Answer: D

20) f(x) = (x + 5) 1/3
A) Relative minimum at (5, 0)
B) Relative minimum at (-5, 0)
C) No relative extrema exist
D) Relative maximum at (-5,0)
Answer: C

3
21) f(x) = x + 1
A) Relative minimum at (1, 0)
B) Relative minimum at (-1, 0)
C) Relative maximum at (-1, 0)
D) No relative extrema exist
Answer: D

22) f(x) = (x + 2)2/3 + 6
A) Relative minimum at (2,6)
B) Relative minimum at (-2, 6)
C) No relative extrema exist
D) Relative maximum at (-2,6)
Answer: B

8
23) f(x) =
1 -6x2
A) Relative maximum at (0, 8)
B) Relative minimum at (2, 8)
C) Relative minimum at (0, 8)
D) No relative extrema exist
Answer: C




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