# How do you determine if rolles theorem can be applied to #f(x) = 2 − 20x + 2x^2# on the interval [4,6] and if so how do you find all the values of c in the interval for which f'(c)=0?

##### 1 Answer

Jun 22, 2015

It is possible to apply and the answer is

#### Explanation:

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=2-20x+2x^2# is a function that is continue in all#RR# , and so it is in#[4,6]# ;#y'=-20+4x# is a function continue in all#RR# , so our function is derivable in all#RR# , so it is in#[4,6]# ;#f(4)=f(6)=-46# .

To find

(the value is