Explanation Given: The function, f ( x ) = x 2 − 2 x 3 Concept Used: The derivative of a function y = f ( x ) using limit definition is given by, f ' ( x ) = lim h → 0 f ( x + h ) − f ( x ) h ( a + b ) 2 = a 2 + 2 a b + b 2 ( a + b ) 3 = a 3 + 3 a 2 b + 3 a b 2 + b 3 Domain of a function is the set of input values for which the function is defined. Calculation: Consider the function, f ( x ) = x 2 − 2 x 3 In order to find the derivative of the function, using the definition of derivatives, it gives f ' ( x ) = lim h → 0 f ( x + h ) − f ( x ) h = lim h → 0 [ ( x + h ) 2 − 2 ( x + h ) 3 ] − ( x 2 − 2 x 3 ) h = lim h → 0 [ ( x 2 + 2 x h + h 2 ) − 2 ( x 3 + 3 x 2 h + 3 x h 2 + h 3 ) ]

15th Edition

ISBN: 9781305420878

Author: Stewart

Publisher: CENGAGE L

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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 25E

To determine

The derivative of the function f(x)=x2−2x3 using the definition of the derivative and state the domain of function and derivative.

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Chapter 3.2, Problem 24E

Chapter 3.2, Problem 26E

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The derivative of the function f ( x ) = x 2 − 2 x 3 using the definition of the derivative and state the domain of function and derivative.

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The derivative of the function f(x)=x2−2x3 using the definition of the derivative and state the domain of function and derivative.

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