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1 answer:
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Answer:
The number of pounds of City Roast Columbian coffee they should buy is 1 and the number of pounds of French Roast Columbian coffee they should buy is 11.
Step-by-step explanation:
Let
x ----> the number of pounds of a City Roast Columbian coffee
y ---> the number of pounds of a French Roast Columbian coffee
we know that
-----> equation A
----> equation B
Solve the system of equations by graphing
The solution is the intersection point both graphs
The solution is the point (1,11)
therefore
The number of pounds of City Roast Columbian coffee they should buy is 1 and the number of pounds of French Roast Columbian coffee they should buy is 11.
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Answer:
- graph is shown below
- absolute max and min do not exist
- local max: 0 at x=0
- local min: -500/27 ≈ -18.519 at x=10/3
Step-by-step explanation:
The function is odd degree so has no absolute maximum or minimum. It factors as ...
g(x) = x^2(x -5)
so has zeros at x=0 (multiplicity 2, meaning this is a local maximum*) and x=5.
Differentiating, we find the derivative of g(x) is zero at x = 0 and x = 10/3.
g'(x) = 3x^2 -10x = x(3x -10) ⇒ x=0 and x=10/3 are critical points
The value of g(10/3) is a local minimum. That value is ...
g(10/3) = (10/3)^2((10-15)/3) = -500/27 ≈ -18.519
__
The local maximum is (0, 0); the local minimum is (10/3, -500/27). The graph is shown below.
_____
* When a root has even multiplicity, the graph does not cross the x-axis. That means the root corresponds to a local extremum. Since this is the left-most root of an odd-degree function with a positive leading coefficient, it is a local <em>maximum</em>. (The function is <em>increasing</em> left of the left-most turning point.)
