Verify Lagranges mean value theorem for function `f(x)=2x^2-3x+1` on `[1,\ 3]` and find a point `' c '` in the indicated interval:

Answer

Proved

Explanation

ATQ,

`f(x)=2 x^{2}-3 x+1` in the interval `[1,3]`

We know that a polynomial functions are continuous at each point also it is differentiable.

So `f(x)` being a polynomial it is continuous and differentiable on points `(1,3)`

So there must exist at least one real number `c \in(1,3)` such that

`f^{\prime}(c)=\frac{f(3)-f(1)}{3-1}=\frac{f(3)-f(1)}{2}`


Given `f(x)=2 x^{2}-3 x+1`

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