A young woman is in the market for a new car and wants to know the mechanics of operations  to save costs over time. The projected rate to help savings for the car is:  C'(x)=223-x2    where x repersents how many years the car will get prime use.   The rate of additional maintence and cost of car is  M'(x) = x2 + 27x +180   Graph both of the rate functions and state the range and domain. For which x does C′(?)=M′(?)? Solve the equation algebraically. What point on the graph does the solution correspond to? What does a solution here mean?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
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A young woman is in the market for a new car and wants to know the mechanics of operations  to save costs over time. The projected rate to help savings for the car is: 

C'(x)=223-x2    where x repersents how many years the car will get prime use.

 

The rate of additional maintence and cost of car is 

M'(x) = x2 + 27x +180

 

Graph both of the rate functions and state the range and domain.

For which x does C′(?)=M′(?)? Solve the equation algebraically.

What point on the graph does the solution correspond to?

What does a solution here mean?

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