l. (Marginal cost, revenue , and profit) Puls ar manu factures a series of 20-inch flat-tube digital televi sions.
The quantity x of these sets demanded each week is related to the wholesale unit price p by
the equat ion p = - 0.003x + 150. The weekly total cost incurred by Pulsar for producing x sets is
C(x) = 0.000004x3 - 0.006x2 + 150x + 60,000 dollars.
a) Find the revenue function R = R(x) and the profit function P = P(x).
b) Find the marginal cost function, the marginal revenue function, and the marginal profit function.
e) How many TVs should be produced to maximize the profit?
2. Refer to the following graph of a function y= f(x):
: ,., ........ .)
a) find the points where f(x) = O
b) find the intervals where f'(x) > O
e) find the intervals where f'(x) < O
d) find the points/intervals where f'(x) = O
e) find the points where f'(x) doesn't exist .
f) find the points/ intervals where f"(x) = O.
j) find the intervals where f"(x) > O.
h) find the intervals where f"(x) < O.
3. Find the interval(s) where the function f(x) is increasing and the int erval(s) where it is decreasing.
x 2 1
b) f(x) = X 2
e) f(x)=J4 - x2
4. Find the relative maxima and relative minima , if any, of each function.
b) f(x) = x2 - 1
e) f ( x) = J x2 + 4x + 4
5. Find the horizontal and vertical asympt otes of the graph of the function.
1 - x
a) f(x) = 1 + x
b) f(x) = x2 - l
x 3 - 2x
c) f(x) = (x - l)(x2 + 1)
A Cuide to Curve Sketching
(a) Determine the domain off.
(b) Find the x - and y- intercepts of f.
(e) Find all horizontal and vertical asymptotes off.
( d) Determine the intervals where f is increasing and where f is decreasing.
(e) Find the relative extrema of f.
(f) Determine the concavity of f.
(g) Find the inflection points of f.
(h) Plot a few additional points to help furth er identify the shape of the graph off and sketch the
6. Sketch the graph of the function, using the curve-sketching guide above and verify the result using
a) f(x) = x2 - 4
b) f(x) x - 4
x + 2
1 - 1 1
These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction
of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.