Question

Your used Chevy's gas mileage (in miles per gallon (mpg) is given as a function M (x) of speed in miles per hour (mph), where M(1) - 2000 Calculate M' (40), M' (50) and M' (60) rounded to two decimal places M' (40) = mpg/mph M' (50) = mpg/mph M' (60) = mpg/mph

Answer 1

$\mbox{We compute M'(x) using quotient rule of differentiation.}\\ \Big(\frac{f}{g} \Big)'= \frac{gf'-fg'}{g^2}.\\ \mbox{The detailed solution is attached below.}$

M)= H000 X+3025x MA 3025 4000X Mx) 3025 + 2-3025). Yo00-(000 x) (21) x.3 02 s)2 M)- Mx) 8 000 x 4000x +121000 00 x 3025) M (x) 12l000 00 (x3025) 000x 1600 M(40121000 00 (1600.3025) 5700 0 2139 0625 0.266471 8773

= 0.27 mbg/mph M(40) Y000 x2500 M(50) 12100 000 (2500+3025 210 30 525625 0-068794 6 602 M'(50) 0-07 mb/mph 4000 x 360o M (60) 12100000 (3600+3025) 4389 0625 0.0520299 0Y mbg/mph M (60) - O.05