The function s (x) equals=startfraction 3600 over 60 plus x endfraction equals 3600 left parenthesis 60 plus x right parenthesis superscript negative 1 3600 60+x=3600 (60+x) - 1 gives a person's average speed in miles per hour if he or she travels one mile in x seconds more or less than 60 seconds. use a linear approximation to s at 0 to find a person's approximate average speed if he or she travels one mile in 5656 seconds. what is his or her exact speed?

Answer: The linear approximation, about x = 0, is as you said, s (x) = s (0) + s' (0) (x - 0) = 60 - x. From that, what is s (51) ? These are some things that I have been trying: x = 51 a = 0 s (0) = 60 s' (0) = - 0.292184076 How in the world did you get this? This appears to be your main error. You said, above, that s' (t) = / frac{-3600}{ (60 + x) ^2}, Setting x = 0 in that gives, as I said before, - 1. s (0) + s' (0) (51 - 0) = 60 - 14.90138787 = 45.098 ... And, x = 0 a = 51 s (0) = 60 s' (0) = - 0.292184076 s (0) + s' (0) (0 - 51) = 60 + 14.90138788 = 74.901 ... It's probably something to do with how I am substituting the values but I haven't been able to arrange them in a way that yields anything close to the answer. I did find something that gave me an answer of 9 when I was playing around with the x - a stuff but I cannot remember what it was that I did. Maybe I need to add the answer of 9 that I found to the s (a) = 60 in order to get 69?