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:

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

then at least one #cin(a,b)# as if #f'(c)=0# exists.

So:

  1. #y=2x^2-5x+1# is a function that is continue in all #RR#, and so it is in #[0,2]#;
  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]#;
  3. #f(0)=1;f(2)=-1rArrf(a)!=f(b)# and so we can't apply the Rolles Theorem.