Keiko is a software saleswoman. Let represent her total pay (in dollars). Let represent the number of copies of History is Fun she sells. Suppose that and are related by the equation .
Answer the questions below.
Note that a change can be an increase or a decrease.
For an increase, use a positive number. For a decrease, use a negative number.
What is the change in Keiko's total pay for each copy of History is Fun she sells?
What is Keiko's total pay if she doesn't sell any copies of History is Fun?
It would help if you proofread your questions before you posted them.
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To find the change in Keiko's total pay for each copy of History is Fun she sells, we need to differentiate the equation relating her total pay and the number of copies she sells.
Given the equation , we can differentiate both sides with respect to to find the derivative of :
.
Differentiating the left side with respect to gives us , as is a constant term.
Differentiating the right side with respect to gives us as the derivative of is .
Therefore, the derivative of with respect to is .
So, the change in Keiko's total pay for each copy of History is Fun she sells is .
To find Keiko's total pay if she doesn't sell any copies of History is Fun (i.e., ), we substitute into the equation :
.
This simplifies to:
.
Hence, Keiko's total pay if she doesn't sell any copies of History is Fun is .