\textbf{120.} The mean value theorem applies to the function $y = \sqrt{21 - x^2 + 4x}$ on the interval $[6,\ 8]$. For the instantaneous rate of change to equal the average rate of change of this function, what value of $x$ is required?
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(1) $4 + \sqrt{7}$ \hfill (2) $3 + 2\sqrt{7}$ \hfill (3) $2 + \dfrac{3}{2}\sqrt{7}$ \hfill (4) $2 + \dfrac{5}{2}\sqrt{7}$
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