Cost, Revenue, and Profit A company produces a product for which the variable cost is $ 12.30 per unit and the fixed costs are $ 98 , 000 . The product sells for $ 17.98 . Let x be the number of units produced and sold. (a) The total cost for a business is the sum of the variable cost and the fixed costs. Write the total cost C as a function of the number of units produced. (b) Write the revenue R as a function of the number of units sold. (c) Write the profit P as a function of the number of units sold. ( Note: P = R − C )
Cost, Revenue, and Profit A company produces a product for which the variable cost is $ 12.30 per unit and the fixed costs are $ 98 , 000 . The product sells for $ 17.98 . Let x be the number of units produced and sold. (a) The total cost for a business is the sum of the variable cost and the fixed costs. Write the total cost C as a function of the number of units produced. (b) Write the revenue R as a function of the number of units sold. (c) Write the profit P as a function of the number of units sold. ( Note: P = R − C )
Solution Summary: The author calculates the total cost of a business as the sum of the variable cost and the fixed costs.
A company produces a product for which the variable cost is
$
12.30
per unit and the fixed costs are
$
98
,
000
.
The product sells for
$
17.98
. Let x be the number of units produced and sold.
(a) The total cost for a business is the sum of the variable cost and the fixed costs. Write the total cost C as a function of the number of units produced.
(b) Write the revenue R as a function of the number of units sold.
(c) Write the profit P as a function of the number of units sold. (Note:
P
=
R
−
C
)
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).
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