(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).

Bundle: Applied Calculus, Loose-leaf Version, 7th + Webassign Printed Access Card For Waner/costenoble's Applied Calculus, 7th Edition, Single-term

7th Edition

ISBN: 9781337604703

Author: Waner, Stefan; Costenoble, Steven

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 5.3, 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).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 5.3, Problem 79E

Chapter 5.3, Problem 81E

Students have asked these similar questions

Use the shell method to find the volume of the solid generated by revolving the region bounded by the curves and lines about the y-axis. y=x², y=7-6x, x = 0, for x≥0

The graph of f(x) is given below. Select all of the true statements about the continuity of f(x) at x = −3. -7-6- -5- +1 23456 1 2 3 4 5 67 Select the correct answer below: ○ f(x) is not continuous at x = f(x) is not continuous at x = f(x) is not continuous at x = f(x) is continuous at x = -3 -3 because f(-3) is not defined. -3 because lim f(x) does not exist. 2-3 -3 because lim f(x) = f(−3). 2-3

Could you explain how this was solved, I don’t understand the explanation before the use of the shift property As well as the simplification afterwards

Chapter 5 Solutions

Bundle: Applied Calculus, Loose-leaf Version, 7th + Webassign Printed Access Card For Waner/costenoble's Applied Calculus, 7th Edition, Single-term

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

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.

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 5 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 5 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 .