Verify Rolles theorem for the function `f(x)=x^2-5x+6` on the interval [2, 3].

Explanation

Given, `f(x)=x^{2}-5 x+6 in [2,3]`

Since,` f(x) `being a polynomial function in `x.`

So, `f(x)` in differential and continuous every where.

So,` f(x)` is continuous in `[2,3]` and derivable is `(2,3)`

Also,` f(2)=0` and `f(3)=0`

`\therefore {f}(2)={f}(3)`

Hence, all the condition of Rolle's theorem are satisfied for f(x) in [2,3]

So, there exist `C \in(2,3)` such that `f^{\prime}(C)=0`

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