Answered: f(x)=x^3-9/x find the second…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

f(x)=x^3-9/x

find the second derivative

Expert Solution

Step 1

$G i v e n f u n c t i o n f (x) = x^{3} - \frac{9}{x} f (x) = x^{3} - 9 x^{- 1} d i f f e r e n t i a t e w i t h r e s p e c t i v e t o x f' (x) = \frac{d}{d x} (x^{3} - 9 x^{- 1}) f' (x) = \frac{d}{d x} (x^{3}) - \frac{d}{d x} (9 x^{- 1}) f' (x) = 3 * x^{3 - 1} - (- 1) 9 x^{- 1 - 1} (\frac{d}{d x} x^{n} = n x^{n - 1}) f' (x) = 3 * x^{2} + 9 x^{- 2} d i f f e r e n t i a t e a g a i n w i t h r e s p e c t i v e t o x f'' (x) = \frac{d}{d x} (3 x^{2} + 9 x^{- 2}) f'' (x) = \frac{d}{d x} (3 x^{2}) + 9 \frac{d}{d x} (x^{- 2}) f'' (x) = 3 * 2 x^{2 - 1} + 9 (- 2) x^{- 2 - 1} f'' (x) = 6 x^{1} - 18 x^{- 3} f'' (x) = 6 x - \frac{18}{x^{3}}$