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17A Practice Midterm 2
(Guy F’07)
1. Differentiate the functions with respect to the independent variable:
a)
g
(
y
)
=
ln tan(
y
)
( )
b)
f
(
N
)
=
r aN
!
N
2
( )
1
!
N
K
"
#
$
%
’
c)
f
(
x
)
=
x
x
2
2. Suppose the stimulusresponse curve of a neuron in the visual cortex of the brain is given by
f
(
x
)
=
bxe
!
ax
,
x
"
0
where
x
is a positive measure of the intensity of the stimulus,
f
(
x
)
is a measure of the activity of the
neuron, and
a
and
b
are positive constants.
a) Determine all intensities at which maximal and minimal neuron activity occurs.
b) For what stimulus intervals is the activity level increasing and decreasing?
c) What is the intensity at which level of activity is decreasing most rapidly?
d) Sketch the graph of
f
(
x
)
and label all local maxima, minima and inflection points.
3. The rate of a biochemical reaction
R
(
x
)
in sec
1
as a function of the concentration of a chemical
x
in
mM is given by
R
(
x
)
=
x
2
x
2
+
1
,
x
!
0
.
a) This reaction rate has been measured and found to fit a linear model well near
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This note was uploaded on 05/31/2011 for the course MATH 17A taught by Professor Lyles during the Spring '08 term at UC Davis.
 Spring '08
 LYLES

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