(a) Explanation Given information: It is provided that a company finds that the number of new products it develops per year depends on the size of its annual R&D budget, x according to the formula n ( x ) = − 1 + 8 x + 2 x 2 − 0.4 x 3 . n ( x ) = − 1 + 8 x + 2 x 2 − 0.4 x 3 Formula used: If a function has a derivative that in turn differentiable, then its second derivative is the derivative of y , written as d 2 y d x 2 . y ″ = d 2 y d x 2 = d d x [ d y d x ] Calculation: Consider the provided equation: n ( x ) = − 1 + 8 x + 2 x 2 − 0.4 x 3 Consider the formula: y ″ = d 2 y d x 2 = d d x [ d y d x ] Differentiate the above equation with respect to s : d n ( x ) d x = d d x ( − 1 + 8 x + 2 x 2 − 0.4 x 3 ) = 0 + 8 + 4 x − 1.2 x 2 Thus, d n d x = 8 + 4 x − 1.2 x 2 Differentiate again the above equation with respect to n : n ″ ( x ) = d 2 n d x 2 = d d x ( 8 + 4 x − 1.2 x 2 ) = 4 − 2 (b) To determine To calculate: The size of the budget which gives the largest rate of return as measured in new products per dollar (again, called the point of diminishing returns).

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

7th Edition

ISBN: 9781337275972

Author: Waner, Stefan; Costenoble, Steven

Publisher: Cengage Learning

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Chapter 12.3, Problem 80E

(a)

To determine

To calculate: The value of n″(1) and n″(3), the interpretation of the result where a company finds that the number of new products it develops per year depends on the size of its annual R&D budget, x according to the formula n(x)=−1+8x+2x2−0.4x3.

(b)

To determine

To calculate: The size of the budget which gives the largest rate of return as measured in new products per dollar (again, called the point of diminishing returns).

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Chapter 12.3, Problem 79E

Chapter 12.3, Problem 81E

Chapter 12 Solutions

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

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The value of n ″ ( 1 ) and n ″ ( 3 ) , the interpretation of the result where a company finds that the number of new products it develops per year depends on the size of its annual R&D budget, x according to the formula n ( x ) = − 1 + 8 x + 2 x 2 − 0.4 x 3 .

Solution Summary: The author calculates that the number of new products a company develops per year depends on the size of its annual R&D budget.

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To calculate: The value of n″(1) and n″(3), the interpretation of the result where a company finds that the number of new products it develops per year depends on the size of its annual R&D budget, x according to the formula n(x)=−1+8x+2x2−0.4x3.

To calculate: The size of the budget which gives the largest rate of return as measured in new products per dollar (again, called the point of diminishing returns).

Want to see the full answer?

Chapter 12 Solutions

The value of n ″ ( 1 ) and n ″ ( 3 ) , the interpretation of the result where a company finds that the number of new products it develops per year depends on the size of its annual R&amp;D budget, x according to the formula n ( x ) = − 1 + 8 x + 2 x 2 − 0.4 x 3 .

Solution Summary: The author calculates that the number of new products a company develops per year depends on the size of its annual R&D budget.

Concept explainers

Videos

To calculate: The value of n″(1) and n″(3), the interpretation of the result where a company finds that the number of new products it develops per year depends on the size of its annual R&D budget, x according to the formula n(x)=−1+8x+2x2−0.4x3.

To calculate: The size of the budget which gives the largest rate of return as measured in new products per dollar (again, called the point of diminishing returns).

Want to see the full answer?

Chapter 12 Solutions

The value of n ″ ( 1 ) and n ″ ( 3 ) , the interpretation of the result where a company finds that the number of new products it develops per year depends on the size of its annual R&D budget, x according to the formula n ( x ) = − 1 + 8 x + 2 x 2 − 0.4 x 3 .