Use a CAS to generate a contour plot of f x , y = 2 y 2 x − y x 2 + 4 x y for − 5 ≤ x ≤ 5 and − 5 ≤ y ≤ 5 , and use the plot to ap-proximate the locations of all relative extrema and saddle points in the region. Check your answer using calculus, and identify the extrema as relative maxima or minima .
Use a CAS to generate a contour plot of f x , y = 2 y 2 x − y x 2 + 4 x y for − 5 ≤ x ≤ 5 and − 5 ≤ y ≤ 5 , and use the plot to ap-proximate the locations of all relative extrema and saddle points in the region. Check your answer using calculus, and identify the extrema as relative maxima or minima .
Solution Summary: The author explains how to graph the function f(x,y) with the following commands in Maple.
f
x
,
y
=
2
y
2
x
−
y
x
2
+
4
x
y
for
−
5
≤
x
≤
5
and
−
5
≤
y
≤
5
,
and use the plot to ap-proximate the locations of all relative extrema and saddle points in the region. Check your answer using calculus, and identify the extrema as relative maxima or minima.
Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .
A simple curve that often makes a good model for the variable costs of a company, as a function of the number of units produced, X, has the form:
y= b₁x+ b₂x^2 b₃x^3
(There is no constant term because fixed costs are not included.)
Consider the following table of recorded variable costs versus units produced for some company: *Picture attached below*
- Find the best-fit model curve (from above) to the data (i.e., the least squares solution). Sketch your model.- Use your curve to estimate the variable costs for producing 1, 3, 11 and 20 items.
Answer the question below:
The student should identify all the relative extrema and saddle points of the given function.
h(a, b) =a* + 3a²b + b² – b
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