## Calculus 10th Edition

The slope at the point $(2, 2)$ is$-2$
The graphical definition of the derivative is the slope at a point; hence, whenever you read slope at a point, you need to find the derivative. To find the derivative of $\frac{8}{x^2}$; rewrite it as $8x^{-2}$ then using the power rule, the derivative is $(8)(-2)(x^{-2-1})$ which when simplified is $-\frac{16}{x^3}$. To find the slope at the required point, substitute the x-coordinate into the derivative. Plugging in 2 in the derivative gives us $-\frac{16}{8}$ which is $-2$.