`f(x) = root(3)(x^2 - 1), (3,2)` Find and evaluate the derivative of the function at the given point.

Textbook Question

Chapter 2, Review - Problem 66 - Calculus of a Single Variable (10th Edition, Ron Larson).
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gsarora17 | (Level 2) Associate Educator

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`f(x)=root(3)(x^2-1)` ` `

`f'(x)=(1/3)(x^2-1)^(1/3-1)(2x)`

`f'(x)=(2x)/(3(x^2-1)^(2/3))`

Therefore the derivative at the point(3,2) can be obtained by plugging in the value of x in the f'(x).

f'(x) at (3,2)=`(2*3)/(3*(3^2-1)^(2/3))`

f'(x) at (3,2) `= 2/8^(2/3)=2/(2^3)^(2/3)`

f'(x) at (3,2) `= 1/2`

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