Explanation Given: Function f ( x ) = 2 x 2 + 3 . 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 ) = 2 x 2 + 3 According to the definition of derivative, we have f ′ ( x ) = lim h → 0 [ 2 ( x + h ) 2 + 3 ] − [ 2 x 2 + 3 ] h f ′ ( x ) = lim h → 0 [ 2 ( x 2 + 2 x h + h 2 ) + 3 ] − [ 2 x 2 + 3 ] h f ′ ( x ) = lim h → 0 [ 2 x 2 + 4 x h + 2 h 2 + 3 ] −

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 3FOT

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Show that f′(x)=4x for the function f(x)=2x2+3.

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Chapter 3, Problem 2FOT

Chapter 3, Problem 4FOT

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The marginal revenue (in thousands of dollars) from the sale of x handheld gaming devices is given by the following function. R'(x) = 4x (x² +26,000) 2 3 (a) Find the total revenue function if the revenue from 125 devices is $17,939. (b) How many devices must be sold for a revenue of at least $50,000? (a) The total revenue function is R(x) = (Round to the nearest integer as needed.) given that the revenue from 125 devices is $17,939.

Use substitution to find the indefinite integral. S 2u √u-4 -du Describe the most appropriate substitution case and the values of u and du. Select the correct choice below and fill in the answer boxes within your choice. A. Substitute u for the quantity in the numerator. Let v = , so that dv = ( ) du. B. Substitute u for the quantity under the root. Let v = u-4, so that dv = (1) du. C. Substitute u for the quantity in the denominator. Let v = Use the substitution to evaluate the integral. so that dv= ' ( du. 2u -du= √√u-4

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Chapter 3 Solutions

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Show that f ′ ( x ) = 4 x for the function f ( x ) = 2 x 2 + 3 .

Solution Summary: The author explains that the function f(x) = 2x 2+3. The definition of derivative is stated as follows.

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Show that f′(x)=4x for the function f(x)=2x2+3.

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Chapter 3 Solutions