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.

Answer 1

I got 30 but it say's I'm not right. :/

Answer 2

@uri @phi

Answer 3

@countonme123

Answer 4

@genius12

Answer 5

@Mashy

Answer 6

@Fifciol

Answer 7

take derivative of this equation with respect to s and compare with zero. You should find one value for s. Substitute that s in equation and the answer pops out

Answer 8

I got 30,025

Answer 9

This is a parabola, that opens down. Hence it will have a maximum. Now note, if a parabola given by the equation \(\bf ax^2+bx+c=0\) opens up/down, its minimum/maximum is always at the vertex. Now the vertex is located at \(\bf (-b/2a, \ f(-b/2a))\), i.e. the x-value of the minimum/maximum will be at -b/2a. In this case, MAXIMUM mileage and since we know that this parabola opens down, the vertex will be the maximum. Now, we know the maximum will occur at \(\bf s=-b/2a=-2.45/2(-0.025)=49\). This implies that the maximum mileage (miles/gallon) occurs when the speed is 49 miles/hr. Now to find the actual maximum value, we find \(\bf f(49)\), i.e. the actual value of the function when s = 49. So plug 49 in and see what you get.

NOTE: You could also use derivatives to find the maximum of the parabola but I didn't feel Calculus was needed here. Had the function been cubic,quartic or any degree higher than 2, then one would use calculus.

@lissa_bug

Answer 10

I got 30.025 as well but my school says it is wrong?

Answer 11

I don't think it's wrong ,what is the answer given to you by school?

Answer 12

I didn't think it was wrong either. It'd this practice test and you answer it and it says you're wrong or not. So you go back and keep fixing it. :P Really stupid school.

Answer 13

*it's

Answer 14

@lalaly

Answer 15

@Fifciol Any other ideas on this one?

Answer 16

30 must be right answer

Answer 17

Maybe it is a glitch in my schools auto grade...