Question

Can someone explain to me how to get the points for this problem.. Determine whether Rolle's theorem applies to the function shown below on the given interval . If so, find the point(s) that are guaranteed to exist by Rolle's theorem. f(x)=sin 4x;[pi/4,pi/2].. Okay, I know that it is continuous and differentiable everywhere and f(a)=f(b) a=pi/4 sin 4*pi/4= sin(pi)=0 b=pi/2 sin 4*pi/2= sin (2pi)=0 Then f(x)=sin 4x =f'(x)= 4 cos(4x)=0 cos(4x)=0 and then you determine when cos=0, which is at pi/2 and 3pi/2. when you multiply pi/2 by 4 you get pi/8 and when you multiply 3pi/2 by 4 you get 3pi/8