Water coming out from a fountain is modeled by the function:

f (x) = - x2+6x+6

Where f (x) represents the height, in feet, of the water from the fountain at different times x, in seconds.

What does the average rate of change of f (x) from x = 2 to x = 5 represent?

a. The water travels an average distance of 4 feet from 2 seconds to 5 seconds.

b. The water travels an average distance of 1 foot from 2 seconds to 5 seconds.

c. The water falls down with an average speed of 2 feet per second from 2 seconds to 5 seconds.

d. The water falls down with an average speed of 1 foot per second from 2 seconds to 5 seconds.

Question

Mathematics

Kayden Alexander

20 July, 11:07

Water coming out from a fountain is modeled by the function:

f (x) = - x2+6x+6

Where f (x) represents the height, in feet, of the water from the fountain at different times x, in seconds.

What does the average rate of change of f (x) from x = 2 to x = 5 represent?

a. The water travels an average distance of 4 feet from 2 seconds to 5 seconds.

b. The water travels an average distance of 1 foot from 2 seconds to 5 seconds.

c. The water falls down with an average speed of 2 feet per second from 2 seconds to 5 seconds.

d. The water falls down with an average speed of 1 foot per second from 2 seconds to 5 seconds.

+3

Answers (2)

Know the Answer?

Orlando Davidson · Answer 1

Average rate of change from x = 2 to x = 5 is (f (5) - f (2)) / (5 - 2) = (( - (5) ^2+6 (5) + 6) - ( - (2) ^2+6 (2) + 6)) / 3 = ((-25+30+6) - (-4+12+6)) / 3 = (11 - 14) / 3 = - 3/3 = - 1

Therefore, the water falls down with an average speed of 1 foot per second from 2 seconds to 5 seconds.

Jordan Lutz · Answer 2

Average speed = change in position / change in time.

m = (f (b) - f (a)) / (b - a)

a = 2, b = 5

f (a) = f (2) = - 4 + 12 + 6 = 14

f (b) = f (5) = - 25 + 30 + 6 = 11

m = (11-14) / (5-2) = - 3/3 = - 1

Answer: D) The water falls down with an average speed of 1 foot per second from 2 seconds to 5 seconds.