Explanation Given: f ( x ) = x 2 − 1 2 x − 3 Concept Used: According to definition of derivative of a function f ( x ) , the derivative of a function f ( x ) is given by: f ′ ( x ) = lim h → 0 f ( x + h ) − f ( x ) h Domain of a function is set of all the points where it is define. Calculation: To find derivative of the function f ( x ) = x 2 − 1 2 x − 3 Use the definition of derivative which states f ′ ( x ) = lim h → 0 f ( x + h ) − f ( x ) h Thus, derivative of given function can be calculated as f ′ ( x ) = lim h → 0 ( x + h ) 2 − 1 2 ( x + h ) − 3 − x 2 − 1 2 x − 3 h = lim h → 0 x 2 + h 2 + 2 x h − 1 ( 2 x + 2 h − 3 ) − x 2 − 1 2 x − 3 h = lim h → 0 ( x 2 + h 2 + 2 x h − 1 ) ( 2 x − 3 ) − ( 2 x + 2 h − 3 ) ( x 2 − 1 ) h ( 2 x + 2 h − 3 ) ( 2 x − 3 ) = lim h → 0 2 x 3 + 2 x h 2 + 4 x 2 h − 2 x − 3 x 2 − 3 h 2 − 6 x h + 3 − 2 x 3 − 2 h x 2 + 3 x 2 + 2 x + 2 h − 3 h ( 2 x + 2 h − 3 ) ( 2 x − 3 ) = lim h → 0 2

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Question

Chapter 3.2, Problem 28E

To determine

To find the derivative of the function

f(x)=x2−12x−3

Also find the domain of the function and the domain of its derivative.

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Chapter 3.2, Problem 27E

Chapter 3.2, Problem 29E

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Chapter 3 Solutions

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To find the derivative of the function f ( x ) = x 2 − 1 2 x − 3 Also find the domain of the function and the domain of its derivative.

Solution Summary: The author explains the definition of derivative of a function f(x) and the domain of its derivative.

Concept explainers

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To find the derivative of the function

f(x)=x2−12x−3

Also find the domain of the function and the domain of its derivative.

Want to see the full answer?

Chapter 3 Solutions

To find the derivative of the function f ( x ) = x 2 − 1 2 x − 3 Also find the domain of the function and the domain of its derivative.

Solution Summary: The author explains the definition of derivative of a function f(x) and the domain of its derivative.

Concept explainers

Videos

To find the derivative of the function f(x)=x2−12x−3 Also find the domain of the function and the domain of its derivative.

Want to see the full answer?

Chapter 3 Solutions

To find the derivative of the function

f(x)=x2−12x−3

Also find the domain of the function and the domain of its derivative.