The first and second derivatives of the function f ( x ) have the values given in Table 1. Find the x -coordinate of all relative extreme points. Find the x -coordinate of all inflection points. Table 1 values of the First two Derivatives of a function x f ' ( x ) f ' ' ( x ) 0 ≤ x ≤ 2 P o s i t i v e N e g a t i v e 2 0 N e g a t i v e 2 < x < 3 N e g a t i v e N e g a t i v e 3 N e g a t i v e 0 3 < x < 4 N e g a t i v e P o s i t i v e 4 0 0 4 < x ≤ 6 N e g a t i v e N e g a t i v e
The first and second derivatives of the function f ( x ) have the values given in Table 1. Find the x -coordinate of all relative extreme points. Find the x -coordinate of all inflection points. Table 1 values of the First two Derivatives of a function x f ' ( x ) f ' ' ( x ) 0 ≤ x ≤ 2 P o s i t i v e N e g a t i v e 2 0 N e g a t i v e 2 < x < 3 N e g a t i v e N e g a t i v e 3 N e g a t i v e 0 3 < x < 4 N e g a t i v e P o s i t i v e 4 0 0 4 < x ≤ 6 N e g a t i v e N e g a t i v e
Solution Summary: The first derivative rule is used to determine the x- coordinates of all relative extreme points.
The first and second derivatives of the function
f
(
x
)
have the values given in Table 1.
Find the
x
-coordinate of all relative extreme points.
Find the
x
-coordinate of all inflection points.
Table 1 values of the First two Derivatives of a function
x
f
'
(
x
)
f
'
'
(
x
)
0
≤
x
≤
2
P
o
s
i
t
i
v
e
N
e
g
a
t
i
v
e
2
0
N
e
g
a
t
i
v
e
2
<
x
<
3
N
e
g
a
t
i
v
e
N
e
g
a
t
i
v
e
3
N
e
g
a
t
i
v
e
0
3
<
x
<
4
N
e
g
a
t
i
v
e
P
o
s
i
t
i
v
e
4
0
0
4
<
x
≤
6
N
e
g
a
t
i
v
e
N
e
g
a
t
i
v
e
Let f(x) and its linear derivative f'(x) be defined for all real numbers. Use the table of selected values to determine f(5).
x
2 3 4
5
f(x)-1?
-13 ?
f'(x)-4-6 ? -10
-19
0-22
O-23
O-31
If f is the function whose graph is shown, let h(x)
f(f(x)) and g(x) = f(x²). Use the graph of f to estimate the value of each derivative.
y
7-
6
5
4
y= fx}
3
2
1
2
3
4
7
(a) h'(2)
(b) g'(2)
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College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning