Question

Water coming out from 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?

Answer 1

F ( x ) = - x² + 5 x + 4
between x = 3 and x = 5:
f ( 3 ) = - 3² + 5 · 3 + 4 = - 9 + 15 + 4 = 10
f ( 5 ) = - 5² + 5 · 5 + 4 = - 25 + 25 + 4 = 4
Average rate of change:
( 4 - 10 ) / ( 5 - 3 ) = - 6 : 2 = - 3 feet / sec