`f(x) = 27/(x^3), (3,1)` Find the slope of the graph of the functions at the given point.

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Chapter 2, Review - Problem 21 - Calculus of a Single Variable (10th Edition, Ron Larson).
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hkj1385 | (Level 1) Assistant Educator

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Note:- 1) If y = x^n ; where n = constant ; then dy/dx = n*x^(n-1)

Now, 

`f(x) = 27/x^3`

`f'(x) = -81/x^4`

``Now, slope of the graph = f'(x) 

Hence slope at (3,1) = f'(3) = `-81/3^4`

`or, f'(3) = -81/81 = -1`

``

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