Explanation Given: Function f ( x ) = x 4 . Formula Used: Definition of derivative is stated as follows: f ′ ( x ) = lim h → 0 f ( x + h ) − f ( x ) h Calculation: Function is given as f ( x ) = x 4 According to the definition of derivative, we have f ′ ( x ) = lim h → 0 ( x + h ) 4 − x 4 h f ′ ( x ) = lim h → 0 x 4 + 4 x 3 h + 6 x 2 h 2 + 4 x h 3 + h 4 − x 4 h f ′ ( x ) = lim h → 0 h

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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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, Problem 6FOT

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Show that f′(x)=4x3 for the function f(x)=x4.

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Chapter 3, Problem 5FOT

Chapter 3, Problem 7FOT

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Show that f ′ ( x ) = 4 x 3 for the function f ( x ) = x 4 .

Solution Summary: The author explains that fprime (x)=4x

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Show that f′(x)=4x3 for the function f(x)=x4.

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Chapter 3 Solutions