# Based on data from the U.S. Bureau of Public Roads, a model for the total stopping distance of a moving car in terms of its speed is s = 1.1v+ 0.054v2, where s is measured in ft and v in mph. The linear term 1.1y models the distance the car travels during the time the driver per-ceives a need to stop until the brakes are applied, and the quadratic term 0.054y2 models the additional braking distance once they are applied. Find ds/dv at v = 35 and v = 70 mph, and interpret the meaning of the derivative.

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Based on data from the U.S. Bureau of Public Roads, a model for the total stopping distance of a moving car in terms of its speed is s = 1.1v+ 0.054v2, where s is measured in ft and v in mph. The linear term 1.1y models the distance the car travels during the time the driver per-ceives a need to stop until the brakes are applied, and the quadratic term 0.054y2 models the additional braking distance once they are applied. Find ds/dv at v = 35 and v = 70 mph, and interpret the meaning of the derivative.

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Step 1

Find ds/dv using first derivative and exponent rule of derivative.

Step 2

To find ds/dv at v = 35 , plug v=35 in ds/dv.

Interpretation: Rate ...

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