Verify Rolle's theorem for the function `f(x)=\ x^2-5x+4\ ` on [1, 4].

Explanation

Rolle`'`s theorem states that if a function `f(x)` is continuous in `[a,b]`and differentiable in interval `(a,b)`, then,

if `f(a) = f(b)`, then ` f'(c) = 0`, where c lies in `(a,b)`.

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

`f(x)` is a quadratic equation and it will be continuous in `[a,b]`.

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

So, `f(x)` is differentiable in `(1,4)`.

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

`f(4) = 4^2-5(4)+4 = 16-20 +4 = 0`

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