First and second derivatives Find ƒ′(x) and ƒ″(x). 72. f(x) =2x +

Answered: 72. f(x) =2 x +

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter2: Functions And Graphs

Section2.CT: Chapter Test

Problem 4CT: Find f(1) and f(2). f(x)=x+7

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First and second derivatives Find ƒ′(x) and ƒ″(x).

Expert Solution

Step 1

Given,

To find

f'(x)=?

f''(x)=?

Step 2

a).

$\frac{d}{d x} [\frac{x}{x + 2}] = \frac{\frac{d}{d x} [x] \cdot (x + 2) - x \cdot \frac{d}{d x} [x + 2]}{{(x + 2)}^{2}} \{a p p l y i n g p r o d u c t r u l e {(\frac{f}{g})}^{'} = \frac{f^{'} g - f g^{'}}{g^{2}}\} = \frac{1 (x + 2) - x (\frac{d}{d x} [x] + \frac{d}{d x} [2])}{{(x + 2)}^{2}} \{b y l i n e a r i t y (f (x) + g (x))' = f' (x) + g' (x)\} = \frac{- x (1 + 0) + x + 2}{{(x + 2)}^{2}} = \frac{2}{{(x + 2)}^{2}} H e n c e f' (x) = \frac{2}{{(x + 2)}^{2}}$

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