Question

Water coming out of a fountain is modeled by the function f(x) = −x2 + 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?

A). The water falls down with an average speed of 3 feet per second from 3 seconds to 5 seconds.

B). The water falls down with an average speed of 5 feet per second from 3 seconds to 5 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 1

Answer:

choice A.   average rate of -3 feet/sec  from 3 sec. to 5 sec

Step-by-step explanation:

f(x) = −x2 + 5x + 4 where f(x) represents the height, in feet,  at x seconds

find average rate of change of f(x)  from x = 3  to x = 5 seconds

find f(3) =  - 3*3 + 5*3  + 4 = -9 + 15 + 4 = 10 feet.

find  f(5) = -5*5 + 5* 5 + 4 =  4 feet.

average rate of change =  (4 - 10)/(5 -3 ) =  -6/2 = -3 feet/sec.

on average  water falls  3 feet /sec  from 3 to 5 seconds   choice A.