## Calculus 10th Edition

The slope at the point $(4, 1)$ is $\frac{1}{4}$.
First rewrite the function as $2-4t^{-1}$. This function is the sum of "smaller" functions hence the overall derivative is the sum of the derivative of the smaller functions. The derivative of 2 is 0. The derivative of $-4t^{-1}$ is equal to $(-4)(-1)(t^{-1-1})$ which is equivalent to $\frac{4}{t^{2}}$. To evaluate the derivative substitute in the x-coordinate. Plugging in $4$ gives us $\frac{4}{16}$ which when simplified is $\frac{1}{4}$.