Question

The highway mileage m in miles per gallon for a compact car is approximated by m(s) = -0.025s2 + 2.45s - 30, where s is the speed in miles per hour. What is the maximum mileage for this compact car to the nearest tenth of a mile per gallon? __________ mi/gal. (Enter the number only.)

To the nearest whole number, what speed results in this mileage? __________ mi/h (Enter the number only.)

Answer 1

differentiate with respect to s and equate it to 0.
you will get the speed for which the mileage is maximum. use that to calculate the mileage.

Answer 2

ok

Answer 3

do i do it to all the s's or the end one?

Answer 4

huh?
do you know how to differentiate?
is this a calculus question?

Answer 5

its a lagebra question

Answer 6

have you done calculus before?

Answer 7

no

Answer 8

i see. this is going to be hard without using derivatives.
have you done parabolas in geometry?

Answer 9

yea

Answer 10

well? this is a down facing parabola. its vertex is at -b/2a
that is the speed which gives maximum mileage.

Answer 11

so speed = -b/2a = -2.45/(2 x - 0.025) = -2.45/-0.05 = 2.45/0.05 = 245/5 = 49 mph

Answer 12

substitute that in the mileage equation and get the maximum mileage.

Answer 13

ok