I am currently studying for a calculus test, and came across a tricky problem in the study guide. I double and triple checked my math, but my answer is not the same as in the study guide answer key. My father recommended I post here for help. The problem is as follows:
A men's suit manufacturer finds that the cost, in dollars, of producing x suits is given by C(x) = 841 + 18√(x) Find the rate at which the average cost is changing when 500 suits have been produced. Round the answer to four decimal places.
My logic that I have repeatedly checked is as follows:
C(x) = 841 + 18√(x) = 18x^(1/2) + 841 C`(x) = 9x^(-1/2) C``(x) = (-9/2)x^(-3/2) = -9/(2x√(x)) C``(500) = -0.000402492 ≈ -$0.0004/suit
The answer that was in the back of the study guide was -$0.0042/suit
I also tried finding C`(500) but am fairly certain that it is not the answer as it gave me a positive answer, and also due to the wording of the problem "rate at which the average cost is changing"
Was this possibly a rounding error on the end of the author of the problem, or am I missing something entirely? Thanks
Note: I just posted this over on math overflow, but was informed in no uncertain terms that this is the forum I need to post on. I have since removed the original post on overflow.