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Assume that $f(x)$ is a real-valued function defined for all real numbers $x$ on an open interval whose center is a certain real number $a$. What does it mean to say that $f(x)$ has a derivative $f^{\prime}(a)$ at $x=a$, and what is the value of $f^{\prime}(a) ?$ (Give the definition of $f^{\prime}(a) .$ )
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