a high speed office copier has an initial price of $1800. a service contract cost $270 for the first year and increases by $100 per year thereafter. it can be shown that over x years the total cost of thecopier is given by C(x)=1800+220x+50X^2
When is the average cost per yr smallest?
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To find when the average cost per year is smallest, we need to find the derivative of the total cost function and set it equal to zero.
Given that the total cost function is:
C(x) = 1800 + 220x + 50x^2
We need to calculate the derivative of C(x) with respect to x:
C'(x) = d(C(x))/dx = 220 + 100x
To find when the derivative is equal to zero, we can set it equal to zero and solve for x:
220 + 100x = 0
Subtracting 220 from both sides:
100x = -220
Dividing both sides by 100:
x = -220/100
x = -2.2
However, since time cannot be negative in this context, we need to consider the positive value of x, which is:
x = 2.2
Therefore, the average cost per year is smallest after approximately 2.2 years.