Compute the average rate of the given function over the spec

Compute the average rate of the given function over the specified interval. F(x) = Squareroot x, [4, 9] Compute the average rate of change of the given function over the specified interval. f(x) = 4x^2, [-5, 5] Compute the average rate of change of the given function over the specified interval. f(x) = x + 2/x - 4, [7, 10]

Solution

1) f(x) = sqrtx ; interval [ 4 , 9]

x = 4 ; f(4) = sqrt4 = 2

x = 9 ; f(9) = sqrt(9) = 3

Avg Rate of function = ( 3 - 2)/( 9 -4) = 1/5

2) f(x) = -4x^2 interval [ -4,4]

x = -4 ; f(-4) = -4*(-4)^2 = -64

x = 4 ; f(4) = -4(4)^2 = -64

Avg Rate of function = ( -64 - (-64) )/( 4 - (-4) ) = 0

3) f(x) = (x +2)/( x -4) ; [ 7 , 10 ]

x = 7 ; f(7) = (7+2)/(7-4) = 9/3 = 3

x = 10 ; f(10) =(10 +2)/(10 -4) = 12/6 = 2

Avg Rate of function = ( 2 - 3)/(10 -7) = -1/3