Respuesta :
Answer:
(a)Max M=16.6, at x=40.33 miles per hour.
(b)Minimum M=10.8 at x=60 miles per hour.
Step-by-step explanation:
The function which represents the miles per gallon obtained at a speed of x miles per hour is given as:
[tex]M(x)=-0.015x^2+1.21x-7.8[/tex], 30≤x≤60
To obtain the absolute maximum and minimum miles per gallon, we find the derivative of M(x), set it equal to zero and solve for the critical points.
[tex]M^{'}(x)=-0.03x+1.21=0\\-0.03x=-1.21\\x=40.33[/tex]
Next, we evaluate the function at the end-points and the critical point.
[tex]M(30)=-0.015(30)^2+1.21(30)-7.8=15\\M(40.33)=-0.015(40.33)^2+1.21(40.33)-7.8=16.6\\M(60)=-0.015(60)^2+1.21(60)-7.8=10.8[/tex]
(a)Thus, the maximum absolute miles per gallon is 16.6 which occurs at a speed of x=40.33 miles per hour.
(b)The minimum absolute miles per gallon is 10.8 which occurs at a speed of x=60 miles per hour.
