Math 1431
LAB session 7
C)(0, 3)
Quiz 13
Example 1:
D)( 1, 3) [ (3, 1)
A)5; 9
B)not applicable
C)2; 4
D)-1; 0; 1
Describe the concavity of the graph of
f (x) = 2x3
6
5x + 10 and find the points of inflection (if any).
Example 2:
f (x) = 2x3
Describe the concavity of the graph of
f (x) =
6
5x + 10
3x
x2
4
and find the points of inflection (if any).
f (x) =
Example 3:
f
3x
x2
4
2
Describe the concavity of the graph of f (x) = 3x + 3 cos (2x) on the interval [0, ⇡].
[0, ⇡]
6
f (x) =
Example 4:
f (x) = 3x2 + 3 cos (2x)
[0, ⇡]
3
Find c so that the graph of f (x) = cx + x
6
1
has a point of inflection at (3,f(3)).
f (x) = cx3 + x
C)2; 4
1
D)-1; 0; 1
fQuestion
(x) = 4x#3
[0, ⇡]
f (x) = 2 sin3 (x) +2 3 sin (x) + 10
f (x) = 3x + 3 cos (2x)
3x2 + 5x
17
f (x) = 5x3
3
3x2 + 4x
11
3
1
f (x) = 2 sin (x) + 3 sin (x) + 10 f (x)
+
x
3 = cx function
Give the intervals (if any) where
the
following
is concave up
f (x) = 2x
5x + 10
f (x) = 5x
3
2
f
(x)
=
cx
+ 3x
11
3x
2
3x + 4x
f (x)f (x)
==
4x32 3x2
x
3
A)( 1,
[0, ⇡] 1
C)(
5
2
6x
4
17
f (x) = 2 sin
(x) + 3 sin (x) + 10
2
1
)
5
B)( 15 , 1)f (x)
= 3x + 3 cos (2x)
3
2
=
5x
3x
3
1 + 4x
D)( 25 , 1)f (x)
f (x) = cx + x
, 1)
3
2
f (x) = 4x
3x
+ 5x
17
f (x)
=2 cx
+ 3x
11
2
f (x) = 2 sin (x)3 + 3 sin (x) + 10
(x) = 5x
B)( 15 ,f 1)
1
A)(
1,
)
Question # 5
3
3x2 + 4x
2 of f (x) = cx2 + 3x
Find c 1so, 1)
that the D)(
graph
C)(
, 1)
5
5
A)4
B)
65
16
C)
9
16
D) 98
6
6
6
2
11
has a point of inflection at (2,f(2)).
Example 5:
The graph of f′(x) is shown below. Give the interval(s) where the graph of f(x) is concave up.
[0, ⇡]
Example 6:
f (x) = cx3 + x
Give the full analysis of the following function f (x) = 4x3
3x2
1
6x
17
f (x) = 2 sin (x)3 + 3 sin (x) + 10
f (x) = 5x3
3x2 + 4x
f (x) = cx2 + 3x
6
2
11
f (x) = 3x2 + 3 cos (2x)
Example
7: = cx3 + x
f (x)
f (x) =
1
f (x) = 2 sin3 (x) + 3 sin (x) + 10
3x2 + 4x
f (x) = cx2 + 3x
x2
4
f (x) = 3x2 + 3 cos (2x)
Give the full3 analysis
of the following function on [0, ⇡]
f (x) = 4x
3x2 6x 17
f (x) = 5x3
3x
11
2
6
6
Example 8:
Given the graph of f′(x) below, where is f(x) increasing?
f (x) = 3x2 + 3 cos (2x)
[0, ⇡]
Question #
f (x) = cx3 + x
1
The graph of f′(x) is shown 3below.
2 Give the interval(s) where the graph of f(x) is concave up.
f (x) = 4x
3x
6x
17
f (x) = 2 sin3 (x) + 3 sin (x) + 10
f (x) = 5x3
3x2 + 4x
f (x) = cx2 + 3x
A)( 1, 15 )
B)( 15 , 1)
C)(
1
, 1)
5
D)( 25 , 1)
A)4
B)
5
16
C)
9
16
A)( 2.2, 0.6) [ (4.1, 1)
C)( 1, 2)
11
2
D) 98
B)( 1, 3) [ ( 1, 2) [ (5.2, 1)
D)(2, 5.2)
6
Question #
The graph of f′(x) is shown below. Give the interval(s) where the graph of f(x) is concave down.
A)( 1, 2)
C)(2, 3)
B)( 1, 3) [ ( 1, 2)
D)( 2.1, 1)