How do you find the slope of a tangent line to the graph of the function f(x)= -5/x^3 at x=6?

1 Answer
Jun 20, 2017

Compute the first derivative.
The slope of the tangent line is equal to the first derivative evaluated at the x coordinate.

Explanation:

Given: f(x)= -5/x^3

The derivative and this is easier to do, if we write the function as:

f(x)= -5x^-3

f'(x) = 15x^-4

The slope, m, of the tangent line at x = 6 is f'(6)

m = 15(6)^-4

m = 5/432