Compare each of the functions shown below: f(x) sine curve with points at 0, 0 and pi over 2, 4 and pi, 0 and 3 pi over 2, negative 4 and 2 pi, 0 g(x) x y 0 0 pi over 2 2 π 0 3 pi over 2 −2 2π 0 h(x) = 2 sin x + 3 Which function has the greatest rate of change on the interval from x = 0 to x = pi over 2 ?

f(x) sine curve with points at 0, 0 and pi over 2, 4 and pi, 0 and 3 pi over 2, negative 4 and 2 pi,0

g(x) x y 0 0 pi over 2 2 π 0 3 pi over 2 −2 2π 0

h(x) = 2 sin x + 3 Which function has the greatest rate of change on the interval from x = 0 to x = pi over 2

The change of f(x) from 0 to π/2 is 4
The change of g(x) from 0 to π/2 is 2
We can rule out g(x). 

As for h(x):
h(0) = 2 sin(0) + 3 = 3
h(π/2) = 2(sin(π/2)) + 3 = 2 + 3 = 5
Change of h(x) from 0 to π/2 is 2. 

Greatest change between 0 and π/2 is found with f(x)