Previous 1 2 3 4 5 6 7 8 9 Next Question 2 of 9 ( point) Wiew.peblem in.a. Appli

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Previous 1 2 3 4 5 6 7 8 9 Next Question 2 of 9 ( point) Wiew.peblem in.a. Applications of vertex of quad equations 4 Question The pressure, , in automobile tires can affeet its wear. Both over-inflated and under-inflated tires can lead to poor performance and poor partioular tire, the number of miles that a tire lasts. y (in thousands), is given by y 0.925x2 + 68.45x-700 whero x is the tire pressure in pounds per square inch (psi) mileage. For one Check Answer Solve It Ask My Instructor Link to Textbook Find the tie pressure that will yield the maximum number of miles thata last Round to the nearest whole unit. b. Find the maximum number of miles that a tire will last if the proper tire pressure is maintained. Round to the nearest thousand miles Part 1 out of 2 a. The tire pressure that will yield the maximum number of miles that a tire will last Save for Later

Explanation / Answer

Ans:

Step 1: Given, the relation between the number of miles a tyre lasts and the tyre pressure is

y = -0.925x2 + 68.45x -700

Step 2: To find tyre pressure x at which number of miles tyre lasts are maximum

Step 3: Calculating the first derivative of y with respect to x

dy/dx = -0.925*(2x) + 68.45

Putting this equal to 0

-0.925*(2x) + 68.45 = 0

-1.85x = -68.45

x = 68.45/1.85

x = 37 psi

Step 4: Calculating the second differential of y

dy/dx = -0.925*(2x) + 68.45

d2y/dx2 = -0.925*2 = -1.85

d2y/dx2 < 0

Hence this is maxima

Therefore, x = 37 psi is the tyre pressure at which the number of miles a tyre will last is maximum

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