A study of driving costs based on 2012 medium-sized sedans found that the averag
ID: 2862958 • Letter: A
Question
A study of driving costs based on 2012 medium-sized sedans found that the average cost (car payments, gas, insurance, upkeep, and depreciation) in cents per mile is approximately:
C(x) = 1910.5/x^1.72 + 42.9 (5 x 20)
Where x (in thousands) denotes the number of miles the car is driven each year.†
(A) Show that the graph of C is concave upward on the interval (5, 20).
___??___
(B) What does your result tell you about the average cost of driving a 2012 medium-sized sedan in terms of the number of miles driven?
Choices:
a. The per-mile cost of driving a 2012 medium-sized sedan decreases as the number of miles driven increases, but at a constant rate.
b. The per-mile cost of driving a 2012 medium-sized sedan is constant as the number of miles driven increases.
c. The per-mile cost of driving a 2012 medium-sized sedan increases as the number of miles driven increases, but at a decreasing rate.
d. The per-mile cost of driving a 2012 medium-sized sedan increases as the number of miles driven increase, but at a constant rate.
e. The per-mile cost of driving a 2012 medium-sized sedan decreases as the number of miles driven increases, but at a decreasing rate.
Explanation / Answer
a)C(x) = (1910.5/x1.72) + 42.9
C'(x) = (1910.58(-1.72)/x1.72+1) + 0
C'(x) = (1910.58(-1.72)/x2.72)
C''(x) = (1910.58(-1.72)(-2.72)/x2.72+1)
C''(x) = 8938.457472/x3.72
in the interval (5,20) C"(x)>0
so graph of C is concave upward on the interval (5, 20).
b)C'(x)<0, C"(x)>0
e. The per-mile cost of driving a 2012 medium-sized sedan decreases as the number of miles driven increases, but at a decreasing rate.
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