Verify Rolles theorem for function `f(x)=x^2-5x+4` on `[1,\ 4]`

Explanation

Given, `f(x)=x^2-5x+4` is a polynomial function which is
continuous and differentiable everywhere and in `[1,4]`


`f(1)=1^2-5+4=0`


`f(4)=4^2-5*4+4=0`


`f(1)=f(4)=0`


All condition of Rolle's theorem is satisfied and so there exist `c in (1,4)` such that `f'(c)=0`


`f(x)=x^2-5x+4`


`f'(x)=2x-5`


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