Question

If f(x) = sin(x/2), then there exists a number c in the interval pie/2 < x < 3pie/2 that satisfies the conclusion of the mean value Theorem. What could be c?

Answer 1

The interval is: (pi/2, 3pi/2)
f'(c) = ( f(3pi/2) - f(pi/2) ) / ( 3pi/2 - pi/2)
Find f'(x). Then plug in all the values and solve for c.