(a) The curve with equation y2 =
x3 + 3x2 is called the
Tschirnhausen cubic. Find an equation of the
tangent line to this curve at the point
(1, 2).
y =
(b) At what points does this curve have horizontal tangents?
(x, y)
=
(smaller y-value)
(x, y)
=
(larger y-value)
(c) Illustrate parts (a) and (b) by graphing the curve and the
tangent lines on a common screen.
Consider the following.
x1
−
2x2
+
3x3
=
3
−x1
+
3x2
−
x3
=
2
2x1
−
5x2
+
5x3
=
3
(a) Write the system of linear equations as a matrix
equation,
AX = B.
x1
x2
x3
=
(b) Use Gauss-Jordan elimination on
[A B]
to solve for the matrix X.
X =
x1
x2
x3
=
Consider the function f(x) = (x2ex)/x .
Determine the interval of increasing/decreasing, concavity, local
max/min, inflection points, and any asymptotes.
Step-by-step solutions would be greatly appreciated. Thank you
for the help!
Choose ALL the statements that are true for
f(x)=12x-x3
a. The graph of f(x) is increasing on (-2,2)
b. f(x) has no inflection point
c. The graph of f(x) is concave downward on (- infinity,0)
d. The graph of f(x) is decreasing on (-2,2)
e. f(x) has an inflection point at x=0
f. The graph of f(x) is concave upward on (-infinity,0)
The demand function for a particular product is given by
D(x)=3x2−7x+110‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√D(x)=3x2−7x+110 dollars, where x is
the number of units sold. What is the marginal revenue when 44
items are sold? Round your answer to 2 decimal places.
D(x)=3x2−7x+110‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√t
thats a suqare root over the numbers