The total stopping distance T of a vehicle is where T is in feet and x is the speed in miles per hour. Use differentials to approximate the percent change in total stopping distance as speed changes from x = 30 to x = 35 miles per hour. Round your answer to one decimal place.
A)16.6%
B)359.0%
C)33.2%
D)116.7%
E)38.7%

Question

The total stopping distance T of a vehicle is  where T is in feet and x is the speed in miles per hour. Use differentials to approximate the percent change in total stopping distance as speed changes from x = 30 to x = 35 miles per hour. Round your answer to one decimal place.
A)16.6% 
B)359.0% 
C)33.2% 
D)116.7% 
E)38.7%

Quizplus · Accepted Answer

We need to find the percent change in T as x changes from 30 to 35 mph. We can use the formula for differentials:
dT = T'(x)dx
where T'(x) is the derivative of T with respect to x, evaluated at x = 30. We can find T'(x) by taking the derivative of T(x) = 11x^2/40 + 22x. We get T'(x) = 11x/20 + 22. Evaluating at x = 30, we get T'(30) = 33.5. Plugging in dx = 5, we get dT = T'(30)dx = 167.5. Therefore, the percent change in T is approximately:
(dT/T) * 100 = (167.5/680) * 100 ≈ 24.6%
The closest answer choice is C (33.2%), which is the best option.

The Total Stopping Distance T of a Vehicle Is