`f(x) = 8/(x^2), (2,2)` Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results.
Rewrite the function so that we can use the power rule to take the derivative.
Take the derivative.
`f'(x)= -2(8) x^-3`
Substitute the given x value from the point into the derivative function.
`f'(2)= -16/2^3= -16/8= -2`
The slope at the point `(2,2)` is `-2` .
We can easily see that the tangent line at point (2,2) will have a negative slope.