In Exercises 9–12 the function gives the cost to manufacture x items. Find the average cost per unit of manufacturing h more items (i.e., the average rate of change of the total cost) at a production lev h = 0 el of x, where x is as indicated and and 1 . Hence, estimate the instantaneous rate of change of the total cost at the given production level x, specifying the units of measurement. (Use smaller values of h to check your estimates.) [ HINT: See Example 1.] C ( x ) = 10 , 000 + 5 x − x 2 10 , 000 ; x = 1 , 000
In Exercises 9–12 the function gives the cost to manufacture x items. Find the average cost per unit of manufacturing h more items (i.e., the average rate of change of the total cost) at a production lev h = 0 el of x, where x is as indicated and and 1 . Hence, estimate the instantaneous rate of change of the total cost at the given production level x, specifying the units of measurement. (Use smaller values of h to check your estimates.) [ HINT: See Example 1.] C ( x ) = 10 , 000 + 5 x − x 2 10 , 000 ; x = 1 , 000
Solution Summary: The author calculates the average rate of change for the function C(x) =10,000+5x-x 210,000, which represents the cost of manufacturing x items.
In Exercises 9–12 the function gives the cost to manufacture x items. Find the average cost per unit of manufacturing h more items (i.e., the average rate of change of the total cost) at a production lev
h
=
0
el of x, where x is as indicated and and 1. Hence, estimate the instantaneous rate of change of the total cost at the given production level x, specifying the units of measurement. (Use smaller values of h to check your estimates.) [HINT: See Example 1.]
C
(
x
)
=
10
,
000
+
5
x
−
x
2
10
,
000
;
x
=
1
,
000
The following table shows total military and arms trade expenditure for a certain country in 2000, 2006, and 2012.
Year t (year since 2000)
0
6
12
Military Expenditure C(t)($ billion)
380
540
660
(a)
Compute the average rate of change of C(t) over the period 2006–2012 (that is, [6, 12]). Be sure to state the units of measurement.
Interpret the average rate of change.
This country's military expenditure increased at an average rate of about between 2006 and 2012.
(b)
Compute the average rate of change of C(t) over the period [0, 12]. Be sure to state the units of measurement. (Round your answer to two decimal places.)
Interpret the average rate of change.
This country's military expenditure increased at an average rate of about between 2000 and 2012.
In Exercises 33-36, determine the direction in which f has maximum rateof increase from P, and give the rate of change in that direction.
Assume the rate of investment is given by the function I (t) = ln t. Compute the total capitalaccumulation between the 1st and the 5th years.
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