Water coming out from a fountain is modeled by the function f(x)= -x^2+5x+4 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=3 to x=5 represent?

Answer 1

A. The water falls down with an average speed of 3 ft./s from three seconds to five seconds.
B. The water falls down with an average speed of 5 ft./s from three seconds to five seconds.
C. The water travels an average distance of 3 feet from 3 seconds to 5 seconds.
D. The water travels an average distance of 5 feet from 3 seconds to 5 seconds.

Answer 2

f ( x ) = - x ^ 2 + 5 x + 4

f ( 3 ) = - 3 ^ 2 + 5 * 3 + 4 = - 9 + 15 + 4 = 10

f ( 5 ) = - 5 ^ 2 + 5 * 5 + 4 = - 25 + 25 + 4 = 4

The average rate of change :

[ f ( 5 ) - f ( 3 ) ] / ( 5 - 3 ) =

( 10 - 4 ) / ( 5 - 3 )

= 6 / 2 = 3

Answer A

Answer 3

Thank you so much!

Answer 4

@bonsnian, -3^2 is NOT -9, it’s 9. -5^2 is NOT -25. You are an idiot. Double check your answers before posting them.

Answer 5

@bonsnian, nevermind I’m a !@#$%^&. !@#$%^& me.

Answer 6

@bonsnian, I used my iPhone calculator (simple calculator)