Explanation Given: f ( x ) = 1.5 x 2 − x + 3.7 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 ) = 1.5 x 2 − x + 3.7 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 ′ ( t ) = lim h → 0 1.5 ( x + h ) 2 − ( x + h ) + 3.7 − ( 1.5 x 2 − x + 3.7 ) h = lim h → 0 1.5 ( x 2 + h 2 + 2 x h ) − x − h + 3

15th Edition

ISBN: 9781305420878

Author: Stewart

Publisher: CENGAGE L

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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 24E

To determine

To find the derivative of the function

f(x)=1.5x2−x+3.7

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

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Chapter 3.2, Problem 23E

Chapter 3.2, Problem 25E

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To find the derivative of the function f ( x ) = 1.5 x 2 − x + 3.7 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).

Concept explainers

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To find the derivative of the function

f(x)=1.5x2−x+3.7

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 ) = 1.5 x 2 − x + 3.7 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).

Concept explainers

Videos

To find the derivative of the function f(x)=1.5x2−x+3.7 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)=1.5x2−x+3.7

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