# 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 -

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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