Which function has the greatest rate of change on the interval from x = 0 to x = pi over 2? f(x) g(x) h(x) all three functions have the same rate of change.

The function that has the greatest rate of change is:

                     g(x)

Step-by-step explanation:

We know that the rate of change from x=a to x=b is determined as:

We are asked to find the rate of change of each of the functions form x=0 to x=pi over 2.

f(x):

We are given that:

and,

Hence,

g(x):

We have:

and

Hence,

h(x):

Now we have:

Also,

Hence, the rate of change is calculated as:

               Hence, the greatest rate of change is:

                                g(x)

Since,