Question

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

Answer 1

If the function is:
f ( x ) = 7 sin x + 1;
f ( 0 ) = 7 * sin (0) + 1 = 0 + 1 = 1
f ( π/2 ) = 7 * sin (π/2) + 1 = 7 * 1 + 1 = 7 + 1 = 8
The rate of change is:
( y2 - y1 ) / ( x2- x1 ) = ( 8 - 1 ) / ( π/2 - 0 ) =
= 7 / π/2 = 14 / π
Answer: The rate of change on the interval from x=0 to x =π/2 is 14/π.