Question 6
Let
.
Calculate
.
Correct!
Correct!

Recall the rule:
Then
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Question 7
Let
. Calculate
. Is it possible to determine the sign
of
?
.
.
.

;
is positive for all
.
Correct!
Correct!
;
is negative for all
.

Recall the rule:
Then
is positive for any value of
. There are two ways to see this:
First,
represents exponential growth, so
is an increasing
function and therefore
for all
.
Second,
.
and
are both
positive, and
is positive for all
, so
for all
.
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Question 8
Let
, for
.
Calculate the derivative of
.
Correct!
Correct!

Recall the rule:
and
We have
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Question 9
For
, calculate
Hint: Before calculating the derivative, use a rule of logarithms to re-write
.
.
Correct!
Correct!

Recall:
and
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Question 10
Let
.
Calculate
.
Correct!
Correct!

Recall:
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Question 11
Let
.
Find
.
Correct!
Correct!

Use the power rule and the rule for the derivative of
to calculate
, then evaluate at
.
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Question 12
Let
.
Calculate the relative rate of change at
.
Correct!
Correct!

Recall that the relative rate of change is
Use the power rule to compute
.
:

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