Consider the function $\displaystyle {f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}}}}$ on the interval $\displaystyle {\left[{2},{10}\right]}$. Find the average or mean slope of the function on this interval.
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By the Mean Value Theorem, we know there exists a $\displaystyle {c}$ in the open interval $\displaystyle {\left({2},{10}\right)}$ such that $\displaystyle {f}'{\left({c}\right)}$ is equal to this mean slope. For this problem, there is only one $\displaystyle {c}$ that works. Find it, and enter the exact value.
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