Instantaneous slope

Question

What is the instantaneous slope of y = -8/x at x = -3

1) -8/3

2) 8/3

3) -8/9

4) 8/9

Answer 1

We get the slope from the 1st derivative.

We are given: y = -8/x at x = -3

For me, it is easier to do derivatives if it's written this way:

y = -8*x^-1

y' = +8*x^-2

If x = -3, we have y' = +8/9

CHECK things like this by plotting---with a graphing calculator or online tool

Answer 2

You can also do this using the Quotient Rule:

Answer is #4