Suppose that (f) is a quadratic polynomial. Prove that for (delta in mathbb{R}), [f(x+delta)=f(x)+delta f^{prime}(x)+frac{1}{2} delta^{2} f^{prime

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Suppose that \(f\) is a quadratic polynomial. Prove that for \(\delta \in \mathbb{R}\),

\[f(x+\delta)=f(x)+\delta f^{\prime}(x)+\frac{1}{2} \delta^{2} f^{\prime \prime}(x) .\]

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