Explanation Given information: The function: f ( x ) = 3 x 2 + 2 x + 1 Calculation: A definition of a derivative is f ' ( x ) = lim h → 0 f ( x + h ) − f ( x ) h Given f ( x ) = 3 x 2 + 2 x + 1 , we have f ' ( x ) = lim h → 0 [ 3 ( x + h ) 2 + 2 ( x + h ) + 1 ] − [ 3 x 2 + 2 x + 1 ] h = lim h → 0 3 x 2 + 6 x h + 3 h 2 + 2 x + 2 h + 1 − 3 x 2 − 2 x − 1 h = lim h → 0 h ( 6 x + 3 h + 2 ) h = lim h → 0 ( 6 x + 3 h + 2 ) =

15th Edition

ISBN: 9781305177291

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 3.2, Problem 45E

To determine

To find: f'(x) and f''(x) and then graph f,f' and f'' on a common screen and check to see if your answers are reasonable.

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Chapter 3.2, Problem 44E

Chapter 3.2, Problem 46E

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Chapter 3 Solutions

Biocalculus: Calculus For Life Sciences

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f ' ( x ) and f ' ' ( x ) and then graph f , f ' and f ' ' on a common screen and check to see if your answers are reasonable.

Solution Summary: The author explains how to find f,f'(x) and graph it on a common screen to see if your answers are reasonable.

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To find: f'(x) and f''(x) and then graph f,f' and f'' on a common screen and check to see if your answers are reasonable.

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Chapter 3 Solutions