Business: average revenue, cost, and profit. Given revenue and cost function R ( x ) = 40 x and C ( x ) = 5 x + 100 , R ( x ) find each for the following. Assume C ( x ) are in dollars and x is the number of lamps produced. [ 1 . 6 ] a. The average cost, the average revenue, and the average profit when x lamps are produced and sold b. The rate at which average cost is changing when 9 lamps are produced Average cost is dropping at approximately $ 1.33 per lamp.
Business: average revenue, cost, and profit. Given revenue and cost function R ( x ) = 40 x and C ( x ) = 5 x + 100 , R ( x ) find each for the following. Assume C ( x ) are in dollars and x is the number of lamps produced. [ 1 . 6 ] a. The average cost, the average revenue, and the average profit when x lamps are produced and sold b. The rate at which average cost is changing when 9 lamps are produced Average cost is dropping at approximately $ 1.33 per lamp.
Solution Summary: The author calculates the average cost, average revenue, and average profit when x lamps are produced and sold.
Business: average revenue, cost, and profit. Given revenue and cost function
R
(
x
)
=
40
x
and
C
(
x
)
=
5
x
+
100
,
R
(
x
)
find each for the following. Assume
C
(
x
)
are in dollars and x is the number of lamps produced.
[
1
.
6
]
a. The average cost, the average revenue, and the average profit when x lamps are produced and sold
b. The rate at which average cost is changing when 9 lamps are produced
Average cost is dropping at approximately
$
1.33
per lamp.
Consider the function f(x) = x²-1.
(a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative.
Show all your steps clearly.
(b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the
graph where x 1 and x->
1+h (for a small positive value of h, illustrate conceptually). Then,
draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the
value you found in part (a).
(c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in
the context of the graph of f(x). How does the rate of change of this function vary at different
points?
1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist,
state that fact.
и
(a) f'(-5)
(b) f'(-3)
(c) f'(0)
(d) f'(5)
2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5)
=
4.
-
3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2)
and f'(2).
Elementary Statistics: Picturing the World (7th Edition)
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