Verify Rolles theorem for function `f(x)=x^2-4x+3` on `[1,\ 3]`

Explanation

`f(x) x^2 -4x+3`
(i) f ( x) is polynomial function
`therefore ` It is contionuous in [1,3]
f(x) =2x-4
Which defined in ] 1,3[.
(iii) Here f(1) `=1^2-4(1)+3=0`
and `f(3) =3^1-4(3)+3=0`
`therefore` f(1) =f(3) Thus the conditions of Rolle's theorem satisfies
Now lef f( c) =0
`rArr 2x-4 =0`
`rArr c=2 in ] 1,3[`
Hence Rolle's theorem verified.