# How do you determine if rolles theorem can be applied to #f(x) = 2x^2 − 5x + 1# on the interval [0,2] 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=2x^2-5x+1# is a function that is continue in all#RR# , and so it is in#[0,2]# ;#y'=4x-5# is a function continue in all#RR# , so our function is derivable in all#RR# , so it is in#[0,2]# ;#f(0)=1;f(2)=-1rArrf(a)!=f(b)# and so we can't apply the Rolles Theorem.