Consider the functions in Exercises 5–8 as representing the value of an ounce of palladium in U.S. dollars as a function of the time t in days. Find the average rates of change of R ( t ) over the time intervals [ t , t + h ] , where t is as indicated and h = 0 , 0.1 , and 0.01 days. Hence, estimate the instantaneous rate of change of R at time t, specifying the units of measurement. (Use smaller values of h to check your estimates.) [ HINT: See Example 1.] R ( t ) = 270 + 20 t 3 ; t = 1
Consider the functions in Exercises 5–8 as representing the value of an ounce of palladium in U.S. dollars as a function of the time t in days. Find the average rates of change of R ( t ) over the time intervals [ t , t + h ] , where t is as indicated and h = 0 , 0.1 , and 0.01 days. Hence, estimate the instantaneous rate of change of R at time t, specifying the units of measurement. (Use smaller values of h to check your estimates.) [ HINT: See Example 1.] R ( t ) = 270 + 20 t 3 ; t = 1
Solution Summary: The author calculates the average rate of change for the function R(t)=270+20t
Consider the functions in Exercises 5–8 as representing the value of an ounce of palladium in U.S. dollars as a function of the time t in days. Find the average rates of change of
R
(
t
)
over the time intervals
[
t
,
t
+
h
]
, where t is as indicated and
h
=
0
,
0.1
,
and 0.01 days. Hence, estimate the instantaneous rate of change of R at time t, specifying the units of measurement. (Use smaller values of h to check your estimates.) [HINT: See Example 1.]
In Exercises 11–18, find the slope of the function’s graph at the given point. Then find an equation for the line tangent to the graph there
Do the graphs of the functions in Exercises 39–44 have any horizontal tangent lines in the interval 0 … x … 2p? If so, where? If not, why not? Visualize your findings by graphing the functions with a grapher.
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.
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