Question

the function g(x)=sinx/x defined on [pi/4,pi/2] satisfies the hypotheses of the Mean Value Theorem. True or False

Answer 1

if g'(x) is also defined on the open interval (pi/4,pi/2) then true

Answer 2

use the quotient rule so [x(cosx) -(sinx)(1)]/x^2

Answer 3

g'(x) is undefined at x=0...which is not in the open interval (pi/4,pi/2) soo...yes the function satisfies the Mean value theorem meaning there exists a number g'(c)= [g(b)-g(a)]/(b-a)