Existing Home Sales The following graph shows the approximate value of home prices and existing home sales in 2006–2010 as a percentage change from 2003, together with quadratic approximations: Home prices and sales of existing homes The quadratic approximations are given by Home prices: P ( t ) = t 2 − 10 t + 41 ( 0 ≤ t ≤ 4 ) Existing home sales: S ( t ) = 1.5 t 2 − 11 t ( 0 ≤ t ≤ 4 ) , where t is time in years since the start of 2006. Use the chain rule to estimate d S d P | t = 2 . What does the answer tell you about home sales and prices? [ HINT: See Quick Examples 6 and 7.]
Existing Home Sales The following graph shows the approximate value of home prices and existing home sales in 2006–2010 as a percentage change from 2003, together with quadratic approximations: Home prices and sales of existing homes The quadratic approximations are given by Home prices: P ( t ) = t 2 − 10 t + 41 ( 0 ≤ t ≤ 4 ) Existing home sales: S ( t ) = 1.5 t 2 − 11 t ( 0 ≤ t ≤ 4 ) , where t is time in years since the start of 2006. Use the chain rule to estimate d S d P | t = 2 . What does the answer tell you about home sales and prices? [ HINT: See Quick Examples 6 and 7.]
Solution Summary: The author calculates the derivative of function x and y using chain rule and states what the answer conveys about home sales and prices.
Existing Home Sales The following graph shows the approximate value of home prices and existing home sales in 2006–2010 as a percentage change from 2003, together with quadratic approximations:
Home prices and sales of existing homes
The quadratic approximations are given by
Home prices:
P
(
t
)
=
t
2
−
10
t
+
41
(
0
≤
t
≤
4
)
Existing home sales:
S
(
t
)
=
1.5
t
2
−
11
t
(
0
≤
t
≤
4
)
,
where t is time in years since the start of 2006. Use the chain rule to estimate
d
S
d
P
|
t
=
2
. What does the answer tell you about home sales and prices? [HINT: See Quick Examples 6 and 7.]
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