The slope of the tangent line to the curve $$ y=\frac{2}{x} $$ at the oint $$ (2,1) $$ is:

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The slope of the tangent line at $$ (2, 1) $$ is $$ -\frac{1}{2} $$. To find the slope of the tangent line to the curve $$ y = \frac{2}{x} $$ at the point $$ (2, 1) $$, we need to compute the derivative of the function $$ y $$ with respect to $$ x $$. The function is given by: $$ y = \frac{2}{x} $$ We can differentiate this using the power rule. First, we rewrite the function as: $$ y = 2x^{-1} $$ Now, we differentiate: $$ \frac{dy}{dx} = 2 \cdot (-1) x^{-2} = -\frac{2}{x^2} $$ Next, we evaluate the derivative at the point $$ x = 2 $$: $$ \frac{dy}{dx} \bigg|_{x=2} = -\frac{2}{(2)^2} = -\frac{2}{4} = -\frac{1}{2} $$ Thus, the slope of the tangent line to the curve $$ y = \frac{2}{x} $$ at the point $$ (2, 1) $$ is: $$ \boxed{-\frac{1}{2}} $$

The slope of the tangent line to the curve \( y=\frac{2}{x} \) at the oint \( (2,1) \) is:

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The slope of the tangent line to the curve \( y=\frac{2}{x} \) at the oint \( (2,1) \) is:

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