Quiz
1 answer:
You might be interested in
(a) It looks like you're saying
Find the critical points of F(x). By the fundamental theorem of calculus,
F'(x) = x - 3x² + 7
The critical points are where the derivative vanishes. Using the quadratic formula,
x - 3x² + 7 = 0 ⇒ x = (1 ± √85)/6
Compute the second derivative of F :
F''(x) = 1 - 6x
Check the sign of the second derivative at each critical point.
• x = (1 + √85)/6 ≈ 1.703 ⇒ F''(x) < 0
• x = (1 - √85)/6 ≈ -1.370 ⇒ F''(x) > 0
This tells us F attains a minimum of
(b) Split up the domain of F at the critical points, and check the sign of F'(x) over each subinterval.
• over (-∞, -1.370), consider x = -2; then F'(x) = -7 < 0
• over (-1.370, 1.703), consider x = 0; then F'(x) = 7 > 0
• over (1.703, ∞), consider x = 2; then F'(x) = -3 < 0
This tells us that
• F(x) is increasing over ((1 - √85)/6, (1 + √85)/6)
• F(x) is decreasing over (-∞, (1 - √85)/6) and ((1 + √85)/6, ∞)
(c) Solve F''(x) = 0 to find the possible inflection points of F(x) :
F''(x) = 1 - 6x = 0 ⇒ 6x = 1 ⇒ x = 1/6
Split up the domain at the inflection point and check the sign of F''(x) over each subinterval.
• over (-∞, 1/6), consider x = 0; then F''(x) = 1 > 0
• over (1/6, ∞), consider x = 2; then F''(x) = -11 < 0
This tells us that
• F(x) is concave up over (-∞, 1/6)
• F(x) is concave down over (1/6, ∞)
The best buy is from dealership A because the fees of dealership B is more expensive
<h3>The add-on options</h3>For the purpose of this exercise, the add-on options to select are:
- Air-conditioning
- Sunroof
- GPS
- Bluetooth
- Power door and window
The total amount of the add-on options is:
Total = $1000 + $500 + $3500 + $500 + $750
Total = $6250
<u>The inequality</u>
This is represented using:
Base price * (1 + Tax) + Fees + Add-on total ≤ 20000
So, we have:
(1 + 6.75%) * x + 751.56 + 6250 ≤ 20000
<u>Solve for x</u>
We have:
(1 + 6.75%) * x + 751.56 + 6250 ≤ 20000
Evaluate the like terms
(1 + 6.75%) * x ≤ 12998.44
Divide both sides by (1 + 6.75%)
x ≤ 12176.52
The solution means that the base price of the car cannot exceed $12176.52 for dealership A
<u>The graph of the possible base price</u>
See attachment
<h3>Dealership B</h3>The total amount of the add-on options is:
Total = $500 + $750 + $2750 + $750 + $500
Total = $5250
<u>The inequality</u>
This is represented using:
Base price * (1 + Tax) + Fees + Add-on total ≤ 20000
So, we have:
(1 + 6.75%) * x + 1524.72 + 5250 ≤ 20000
<u>Solve for x</u>
We have:
(1 + 6.75%) * x + 1524.72 + 5250 ≤ 20000
Evaluate the like terms
(1 + 6.75%) * x ≤ 13225.28
Divide both sides by (1 + 6.75%)
x ≤ 12389.02
The solution means that the base price of the car cannot exceed $12389.02 for dealership B
<u>The graph of the possible base price</u>
See attachment
<h3>Where to buy from</h3>Buy from dealership A because the fees of dealership B is more expensive
Read more about inequality at:
#SPJ1
