CALCULUS I Worksheet #69 1. Find all inflection points for f(x) = 2x3

Transcription

CALCULUS I Worksheet #69 1. Find all inflection points for f(x) = 2x3
1.
2.
3.
4.
CALCULUS I
Worksheet #69
3
Find all inflection points for f(x) = 2x + 6x2 – 6x + 7.
Find the maximum value of y = – x2 + 4x + 25 on [–2,3]. (Find the y number at the absolute maximum
point)
Find the absolute minimum value (the y number) of f(x) = x3 – 6x2 on [1,2].
Which point on the graph of f(x) is f ' (x) < 0 and f " (x) > 0?
y
C
D
E
x
A
B
5
1–x
The curve of y = x – 3 is concave down on what interval?
6.
7.
8.
Find all critical points for f(x) = 3x4 + x3.
On what intervals is f(x) = 2x3 + 3x2 increasing?
A couple has enough wire to construct 160 ft of fence. They wish to use it to form three sides of a
rectangular garden, one side of which is along a building. Find the dimensions that will yield the largest
area.
Which point on the graph of f(x) from problem #4 is f ' (x) = 0 and f " (x) > 0?
Which point on the graph of f(x) from problem #4 is f ' (x) > 0 and f " (x) > 0?
If the first derivative of f is negative for x = 9, which of the following statements must be true?
9.
10.
11.
I. f(9) is negative
12.
13.
II.
f has a minimum at x = 9
III.
f is decreasing at x = 9
(A) I only
(B) II only
(C) III only
(D) I & II
(E) I & III
Find all vertical and horizontal asymptotes, x- and y-intercepts, holes, and sketch
x2 – 3x + 2
.
y= 2
x – 4x + 3
x2
Find F ' (x) if F(x) =
∫ 3sint dt
2
4
14.
15.
Find the volume of the solid if the area bounded by y = 3x – x2 and y = x is revolved around the y-axis
The base of a solid in the xy-plane is the circle x2 + y2 = 16. Cross sections of a solid perpendicular to
the y=axis are squares. The volume of the solid is
16π
16
1024
1024π
A) 3
B) 1024π
C) 3
D) 3
E)
3
Answers:
1. (–1,17)
2. 29
4. a
5. x > 3
7. x < –1 and
x>0
8.
w = 40
l = 80
11. C
10. B
13. 6x sin x4
14.
8π
3
3. –16
(Note: x = 0 and 4 are not on the
interval)
⎛ −1 −1 ⎞
6. (0,0) terrace; ⎜ ,
⎟ rel min
⎝ 4 256 ⎠
9. E
⎛ 1⎞
12. va: x = 3; ha: x = 1; hole ⎜1, ⎟ ;
⎝ 2⎠
⎛ 2⎞
y-int: ⎜ 0, ⎟ ; x-int: (2,0)
⎝ 3⎠
15. D

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