Check work Please ?
Find all numbers c that satisfy the conclusion of Rolle's Theorem for the following function and interval. Enter the values in increasing order and enter N in any blanks you don't need to use
f(x)=5sin(2πx) , [-1,1]
f(1)=5sin(2π(1))=0
f(-1)=5sin(2π(-1))=0
f(b)-f(a) / b-a = 0/2 = 0
f'(c)=0
f'(x)=10πcos(2πx)=0
roots are n-1/4
but I can't figure this out

Question

Check work Please ?
Find all numbers c that satisfy the conclusion of Rolle's Theorem for the following function and interval. Enter the values in increasing order and enter N in any blanks you don't need to use
f(x)=5sin(2πx) , [-1,1]
f(1)=5sin(2π(1))=0
f(-1)=5sin(2π(-1))=0
f(b)-f(a) / b-a = 0/2 = 0
f'(c)=0 
f'(x)=10πcos(2πx)=0 
roots are n-1/4  
but I can't figure this out