In Exercises 91–96 , the graph of a derivative f ′ is shown. Use the information in each graph to determine where f is increasing or decreasing and the x -values of any extrema. Then sketch a possible graph of f . Increasing on ( − ∞ , 2 ) , decreasing on ( 2 , ∞ ) , relative minimum at x = 2 .
In Exercises 91–96 , the graph of a derivative f ′ is shown. Use the information in each graph to determine where f is increasing or decreasing and the x -values of any extrema. Then sketch a possible graph of f . Increasing on ( − ∞ , 2 ) , decreasing on ( 2 , ∞ ) , relative minimum at x = 2 .
Solution Summary: The author analyzes the graph of the derivative function fprime and determines whether the function is decreasing or increasing.
In Exercises 91–96, the graph of a derivative
f
′
is shown. Use the information in each graph to determine where f is increasing or decreasing and the x-values of any extrema. Then sketch a possible graph of
f
.
Increasing on
(
−
∞
,
2
)
, decreasing on
(
2
,
∞
)
, relative minimum at
x
=
2
.
EXAMPLE 3
Find
S
X
√√2-2x2
dx.
SOLUTION Let u = 2 - 2x². Then du =
Χ
dx =
2- 2x²
=
信
du
dx, so x dx =
du and
u-1/2 du
(2√u) + C
+ C (in terms of x).
Let g(z) =
z-i
z+i'
(a) Evaluate g(i) and g(1).
(b) Evaluate the limits
lim g(z), and lim g(z).
2-12
(c) Find the image of the real axis under g.
(d) Find the image of the upper half plane {z: Iz > 0} under the function g.
k
(i) Evaluate
k=7
k=0
[Hint: geometric series + De Moivre]
(ii) Find an upper bound for the expression
1
+2x+2
where z lies on the circle || z|| = R with R > 10. [Hint: Use Cauchy-Schwarz]
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
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