What is the rate of change between the interval of x = 0 and x = π/2?

Solution:

The rate of change of function within a given domain interval is defined as the difference between the value of the function at the upper limit of the domain and the value of the function at the lower limit of the domain divided by the difference in the domain limits.

Mathematically stated

Rate of change function F’(X) = F(X_UL) - F(X_LL) / X_UL - X_LL --- (1)

X_UL = Upper limit of the interval for which the rate of change of function is being estimated or calculated

X_LL = Lower limit of the interval for which the rate of change of function is being estimated or calculated

F(X_UL) = Value of the function at X = X_UL

F(X_LL) = Value of the function at X = X_LL

Using the above relationship, the rate of change of the function represented by the graph given above for the interval is given by the relationship:

Rate of Change = [F(π/2) - F(0)]/(π/2 - 0) = (5 - 3)/(π/2) = 4/π

What is the rate of change between the interval of x = 0 and x = π/2?

Summary:

The rate of change between the interval of x = 0 and x = π/2 is 4/π.