A vendor at a carnival sells cotton candy and caramel apples for $ 2.00 each. The vendor is charged $ 100 to set up his booth. Furthermore, the vendor's average cost for each product he produces is approximately $ 0.75 . a. Write a linear cost function representing the cost C x in $ to the vendor to produce x products. b. Write a linear revenue function representing the revenue R x in $ for selling x products. c. Determine the number of products to be produced and sold for the vendor to break even. d. If 60 products are sold, will the vendor make money or lose money?
A vendor at a carnival sells cotton candy and caramel apples for $ 2.00 each. The vendor is charged $ 100 to set up his booth. Furthermore, the vendor's average cost for each product he produces is approximately $ 0.75 . a. Write a linear cost function representing the cost C x in $ to the vendor to produce x products. b. Write a linear revenue function representing the revenue R x in $ for selling x products. c. Determine the number of products to be produced and sold for the vendor to break even. d. If 60 products are sold, will the vendor make money or lose money?
A vendor at a carnival sells cotton candy and caramel apples for
$
2.00
each. The vendor is charged
$
100
to set up his booth. Furthermore, the vendor's average cost for each product he produces is approximately
$
0.75
.
a. Write a linear cost function representing the cost
C
x
in $
to the vendor to produce
x
products.
b. Write a linear revenue function representing the revenue
R
x
in $
for selling
x
products.
c. Determine the number of products to be produced and sold for the vendor to break even.
d. If
60
products are sold, will the vendor make money or lose money?
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).
College Algebra with Modeling & Visualization (5th Edition)
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