Before doing this assignment, do the practice problem posted under Apply and Discover.
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QSO 510: Module 7 Homework
Notes:
1. Before doing this assignment, do the practice problem posted under Apply and Discover.
2. Word-process your solutions within this template. Do not create a new file.
3. Complete all 7 steps. Place work and answers, below each respective step. Expand the space as needed.
4. Show all steps used in arriving at the final answers. Incomplete solutions will receive partial credit.
5. Word-process formulas using Equation Editor and diagrams using Drawing Tool.
Problem 1
Given y = f(x) = x2 + 2x +3
a) Use the definitional formula given below to find the derivative of the function.
Here,
b) Find the value of the derivative at x = 3.
Value of the derivative at X=3 is (2*3+2) =8
Problem 2
Given, y = f(x) = 2 x3 - 3x2 + 4x +5
a) Use the Power function to find derivative of the function.
Using the power function the derivative is,
f’(x) = 6x2 – 6x +4
b) Find the value of the derivative at x = 4.
The value of the derivative at x = 4 is,
f’(4) = 6*42 – 6*4 +4 =76
Problem 3
The revenue and cost functions for producing and selling quantity x for a certain production facility are given below.
R(x) = 16x – x2
C(x) = 20 + 4x
a) Determine the profit function P(x).
The profit function is,
P(X) = R(X) – C(X) = 16x-x2 -20 -4x = 12x-x2-20.
b) Use Excel to graph the functions R(x), C(x) and P(x) for the interval 0≤ x ≤ 12. Copy and paste the graph below. Note: Use Scatter plot with smooth lines and markers.
The required graph is given below,
c) Compute the break-even quantities.
The break even quantity is that point when P(x)=0.
Thus the break-even point is,
12x- x2-20 = 0
Which gives,
X =10 or 2.
d) Determine the average cost at the break-even quantities.
The average costs at breakeven quantities are (20+4*10)/10 = 6 or (20+4*2)/2 = 14.
e) Determine the marginal revenue R’(x).
The marginal revenue is,
R’(x) = = 16-2x
f) Determine the marginal cost C’(x)
The marginal cost is,
C’(x) = = 4
g) At what quantity is the profit maximized?
Note that
P’(X) = 0
· 12- 2x = 0
· X=6
Thus profit is maximized at quantity 6.
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