What is the rate of change for f(x) = 7 sin x - 1 on the interval from x = 0 to x = pi over 2?

Solution:

The average rate of change of a function f(x) is equivalent to the slope of the secant line connecting the two points on the function on the interval [a, b]. It can be expressed as:

average rate of change = [f(b) - f(a)] / b - a

f(π/2) = 7 × sin (π/2) - 1

= 7 × 1 - 1 = 6

f(0) = 7 × sin(0) - 1

= 0 - 1 = - 1

[f(π/2) - f(0)] / π/2 - 0

=  (6 + 1) / (π / 2 - 0)

= 14 / π

The rate of change = (6 + 1) / (π / 2 - 0) = 14/ π.

What is the rate of change for f(x) = 7 sin x - 1 on the interval from x = 0 to x = pi over 2?

Summary:

The rate of change for the function f(x) = 7 sin x - 1 on the interval from [0, π/ 2] is 14/ π.