Answer:
Step-by-step explanation:
<h3>
Answer: 15x^(7/3) - 8x^(7/4) + x + 9000</h3>
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Explanation:
If you know the cost function C(x), to find the marginal cost, we apply the derivative.
Marginal cost = derivative of cost function
Marginal cost = C ' (x)
Since we're given the marginal cost, we'll apply the antiderivative (aka integral) to figure out what C(x) is. This reverses the process described above.


D represents a fixed constant. I would have used C as the constant of integration, but it's already taken by the cost function C(x).
To determine the value of D, we plug in x = 0 and C(x) = 9000. This is because we're told the fixed costs are $9000. This means that when x = 0 units are made, you still have $9000 in costs to pay. This is the initial value. You'll find that all of this leads to D = 9000 because everything else zeros out.
Therefore, we go from this

to this

which is the final answer.
Line segment of length k is divided into 3 equal parts.
so first segment is 0-k/3 and third segment is 2/3k-k
so mid-pt of 1st = k/6 and 3rd = 5/6k
so the distance in between = 5/6k-k/6 = 4/6k = 2/3k
Let
x-------> the width of the rectangular area
y------> the length of the rectangular area
we know that
y=x+15------> equation 1
perimeter of a rectangle=2*[x+y]
2x+2y <= 150-------> equation 2
substitute 1 in 2
2x+2*[x+15] <=150--------> 2x+2x+30 <=150----> 4x <=150-30
4x <= 120---------> x <= 30
the width of the rectangular area is at most 30 ft
y=x+15
for x=30
y=30+15------> y=45
the length of the rectangular area is at most 45 ft
see the attached figure
the solution is<span> the shaded area</span>