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

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Answer 1 · 2017-06-20T13:59:59

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

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#