Final answer:
To find the speed at 47 minutes for the function f(x)=4x^2-8x+5, convert minutes to hours and then take the derivative to get the speed function. Substitute 47/60 hours into the derivative to get the speed, which in this case is -1.73 mph, indicating deceleration.
Step-by-step explanation:
The student is asking to find out the speed in miles per hour (mph) of a person running according to the function f(x)=4x2-8x+5, where f(x) represents miles and x represents hours. To find the speed at 47 minutes, we must first convert 47 minutes to hours. There are 60 minutes in an hour, so 47 minutes is 47/60 hours.
The next step is to calculate the derivative of f(x), which will give us the speed function. Taking the derivative:
- f'(x) = d/dx (4x2 - 8x + 5)
- f'(x) = 8x - 8
Now, we'll substitute x with 47/60 to find the speed at that time:
- f'(47/60) = 8(47/60) - 8
- f'(47/60) = 6.27 - 8
- f'(47/60) = -1.73 mph
This negative value might appear incorrect, but it indicates that the person is slowing down at that moment. Always check if the speed is reasonable and has the correct units and sign.