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?

Solution:[tex]S(x)=\frac{3600}{60+x}-1\\\\ S'(x)= 3600\times\frac{-1}{(60+x)^2}[/tex]If , y = [tex]\frac{1}{x}, {\text{then y' means it's derivative}= \frac{-1}{x^2}[/tex]As average speed = Rate of change of distancefor s=0 , 3600=60+xx= 3540 secondsfor s= 1 mile, x= 5656 secondsAs , average speed =  [tex]\frac{S_{2}-S_{1}}{t_{2}-t_{1}}=\frac{1-0}{5656-3540}=\frac{1}{2116}[/tex]m/sec=0.0004725 m/sec