Question

part 2 short answers:

1) given that g(2)= 5 and g'(2)=3. linearize g(x) near x=2 and use that linearization to approximate g(2,3)

2) the marginal cost in dollars is given by dC/dx = 4x+3. if the fixed costs are 2000, what is the cost of producing 20 units?

Answer #1

The marginal cost in dollars is given by dc/dx=4x +3. If the
fixed costs are $2000 what is the cost of producing 30 units

The weekly cost (in dollars) of producing x compact discs is
given by
C(x) = 2000 + 2x − 0.0001x^2
,
where x stands for the number of units produced. What is the
actual cost incurred in producing
the 2001st disc? What is the marginal cost when x = 2000?

The weekly cost (in dollars) of producing x compact discs is
given by C(x) = 2000 + 2x − 0.0001x^2,
where x stands for the number of units produced. What is the
actual cost incurred in producing the 1001st disc? What is the
marginal cost when x = 1000?

The marginal revenue of a company is given by
r(x)=x^3-0.3x^2+0.1 and the marginal cost is given by
c(x)=x\sqrt{-x^2+100} both measured in thousands of dollars per
hundred units (x) produced. Find the total profit for x=1 to x=4
hundred units produced.

assume that revenue, R(x), and cost, C(x), of producing x units
are in dollars:
R(x)=9x-2x^2 C(x)=x^3 - 3x^2 +4x +1
how many units must be produced to maximize profit? what is the
maximum profit as a dollar amount?

7. Suppose the cost, in dollars, of producing x items is given
by the function C(x) = 1/6x3+ 2x2+ 30.
Current production is at x = 9 units.
(a) (3 points) Use marginal analysis to find the marginal cost
of producing the 10th unit.
(b) (3 points) Find the actual cost of producing the 10th
unit.

3) The marginal cost for producing x items can be given by the
formula: C ′ ( x ) = 350 − 0.18 x. Find the total cost function if
the cost of making 300 items is known to be $97,400.
a) What are the fixed costs?
b) How much would it cost to make 500 items?

1. Given f(x)=2x^3-3x^2+4x+2, find (f^(-1))'(14).
Differentiate and Simplify
2. f(x)=ln(3x) e^(-x^2 ) (Answer with positive exponents
Integrate and Simplify 3. ∫▒(6x^2-5x)/√x dx

x
g(x)
g'(x)
g''(x)
g'''(x)
g^(4)(x)
2
17
22
20
14
5
3
50
160/3
141/34
21
151/8
a) write the third degree taylor polynomial P3 for g(x) at x=3
and use it to approximate g(3.1). Calc permitted
b) Use the Lagrange error bound to show that
Ig(3.1)-p3(3.1)I<0.0006

A major factory has costs each month given by the equation C(x)
= x^2 − 4x + 5 where C is in terms of millions of dollars and x is
the number of part time workers they employ in terms of 100. If the
factory floor has room for at most 300 part time workers, how many
part time workers should they employ if they wish to minimize their
monthly costs? Only answers that utilize the tools of calculus will...

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