Question

Scientists determined that the rate y (in calories per minute) at which you use energy while walking can be modeled by y=0.00849(x-90.2)2 +51.3 where x is your walking speed (in meters per minute). What speed minimizes energy use?

a. 90.2 m/min
b. 51.3 m/min
c. 45.6 m/min
d. 22.8 m/min

Answer 1

Option (a), To find the speed that minimizes energy use, we need to find the minimum value of the given function. Taking the derivative and setting it equal to zero, we find that the speed is 90.2 m/min.

Step-by-step explanation:

To find the speed that minimizes energy use, we need to find the minimum value of the function y = 0.00849(x - 90.2)2 + 51.3. This function represents the rate of energy use while walking.

We can use calculus to find the minimum value.

Taking the derivative of the function with respect to x, we get dy/dx = 2 * 0.00849(x - 90.2).

Setting dy/dx equal to zero and solving for x, we find that x = 90.2.

Therefore, the speed that minimizes energy use is 90.2 m/min.