Question

Find the minimum value of the average cost for the given cost function on the given intervals.

Upper C left parenthesis x right parenthesis equals x cubed plus 36 x plus 432C(x)=x3+36x+432

Answer #1

Find the minimum value of the average cost for the given cost
function on the given intervals.
C (x) = x^3 + 33x + 432
a. 1 ≤ x ≤ 10
b. 10 ≤ x ≤ 20

The cost, in dollars, of producing x belts is given by Upper C
left parenthesis x right parenthesis equals 805 plus 18 x minus
0.075 x squared. The revenue, in dollars, of producing and
selling x belts is given by Upper R left parenthesis x right
parenthesis equals 31 x Superscript six sevenths . Find the rate at
which average profit is changing when 676 belts have been produced
and sold. When 676 belts have been produced, the average profit...

A keyboarder's speed over a 55-min interval is given by the
following function, where Upper W left parenthesis t right
parenthesis W (t) is the speed, in words per minute, at time
t.
Upper W left parenthesis t right parenthesis W(t)equals=negative
3 t squared plus 6 t plus 45
a) Find the speed at the beginning of the interval.
b) Find the maximum speed and when it occurs.
c) Find the average speed over the 55-min interval.

A record club has found that the marginal profit,
Upper P prime left parenthesis x right parenthesisP′(x) ,
in cents, is given by
Upper P prime left parenthesis x right parenthesis equals
negative 0.0008 x cubed plus 0.35 x squared plus 52.9
xP′(x)=−0.0008x^3+0.35x^2+52.9x
for
x less than or equals x≤400 ,
where x is the number of members currently enrolled in the club.
Approximate the total profit when
240 members are enrolled by computing the sum
Summation from i equals...

The vector field F with rightwards arrow on top left parenthesis
x comma y right parenthesis equals open angle brackets s e c
squared x comma space 3 y squared close angle brackets is
conservative.
Find f left parenthesis x comma y right parenthesis such that F
with rightwards arrow on top equals nabla f .
a.
f equals 2 space s e c x plus 6 y
b.
f equals y tan x plus x y cubed...

Let X represent the number of homes a real estate agent sells
during a given month. Based on previous sales? records, she
estimates that
Upper P left parenthesis 0 right parenthesis equals
0.63P(0)=0.63?,
Upper P left parenthesis 1 right parenthesis equals
0.24P(1)=0.24?,
Upper P left parenthesis 2 right parenthesis equals
0.09P(2)=0.09?,
Upper P left parenthesis 3 right parenthesis equals
0.03P(3)=0.03?,
Upper P left parenthesis 4 right parenthesis equals
0.01P(4)=0.01?,
with negligible probability for higher values of
x.a. Explain why it...

Utility function of an individual is given by begin mathsize
12px style U equals f left parenthesis x comma y right parenthesis
equals X cubed Y to the power of 4 end style. find out the optimal
quantities of the two goods, if it is given that price of good X is
N$8 per unit and price of good Y is N$4 per unit and income of the
individual is equal to N$1200?

The cost C, in dollars, of renting a moving truck for a day is
given by the function
Upper C left parenthesis x right parenthesis equals 0.25 x plus
40 comma
where x is the number of miles driven.
(a) What is the cost if a person drives
x equals 200
miles?
(b) If the cost of renting the moving truck is
$150
,
how many miles did the person drive?
(c) Suppose that a person wants the cost to...

The marginal cost of a product can be thought of as the cost of
producing one additional unit of output. For example, if the
marginal cost of producing the 50th product is $6.20, it cost
$6.20 to increase production from 49 to 50 units of output. Suppose
the marginal cost C (in dollars) to produce x thousand mp3 players
is given by the function Upper C left parenthesis x right
parenthesis equals x squared minus 120 x plus 7500.C(x) =...

Find the absolute maximum and absolute minimum for f left
parenthesis x right parenthesis space equals space fraction
numerator x over denominator x squared minus x plus 1 end fraction
on the closed interval between 0 and 3

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