For a certain automobile,

Upper M left parenthesis x right parenthesis equals negative . 015 x squared plus 1.21 x minus 7.8M(x)=−.015x2+1.21x−7.8,

30 less than or equals x less than or equals 6030≤x≤60,

represents the miles per gallon obtained at a speed of x miles per hour.

(a) Find the absolute maximum miles per gallon and the speed at which it occurs.

(b) Find the absolute minimum miles per gallon and the speed at which it occurs.

(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:

, 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.

Next, we evaluate the function at the end-points and the critical point.

(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.

step-by-step explanation:

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step-by-step explanation:

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