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Calculus

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Your Porsche's gas mileage (in miles per gallon) is given as a function M(x) of speed x in miles per hour. It is found that
M'(x) =
3,600x−2 − 1/
(3,600x−1 + x)2.

Estimate M'(10), M'(60), and M'(90). (Round your answers to seven decimal places.)
M'(10) = mpg/mph
M'(60) = mpg/mph
M'(90) = mpg/mph

  • Calculus - ,

    I will read that as

    M'(x) = (3600x^-2 - 1)/(3600x^-1 + x)^2

    which is
    = (3600/x^2 - 1)/(3600/x + x)^2

    M'(10) = (3600/100 - 1)/(3600/10+ 10)^2
    = 35/(370)^2
    = ????

    This makes no sense
    Either I did not interpret your typing correctly, or there is a typo.
    Please use ^ to exponents and brackets to establish where the division is.
    e.g. is it
    (3600x^-2 - 1)/(3600x^-1 + x)^2
    or
    3600x^-2 - ( 1/(3600x^-1 + x)^2 ) ?

  • Calculus - ,

    ok, maybe this is more accurate...

    M'(x) = (3600x^-2 -1)/
    (3600x^-1 +x)^2

  • Calculus - ,

    you plug in 10,60,90 for x
    so
    3600(10)^-1 -1
    /
    (3600(10)^2 +10)^2 = 0.0002557 round to the seven decimal places also and you do that for each one.

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