# How do you determine if rolles theorem can be applied to #f(x)= 10 sin (2x)# on the interval [0,2pi] and if so how do you find all the values of c in the interval for which f'(c)=0?

##### 1 Answer

May 29, 2015

The Rolles theorem says that if:

#y=f(x)# is a continue function in a set#[a,b]# ;#y=f(x)# is a derivable function in a set#(a,b)# ;#f(a)=f(b)# ;

then at least one

So:

#y=10sin(2x)# is a function that is continue in all#RR# , and so it is in#[0,2pi]# ;#y'=20cos(2x)# is a function continue in all#RR# , so our function is derivable in all#RR# , so it is in#[0,2pi]# ;#f(0)=f(2pi)=0# .

To find

and

(both the values are