`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.

Expert Answers
kalau eNotes educator| Certified Educator

Rewrite the function so that we can use the power rule to take the derivative.

`f(x)= 8x^-2`

Take the derivative.

`f'(x)= -2(8) x^-3`

`f'(x)= -16/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.