Answered: Assume that it costs a company…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section2.4: Average Rate Of Change Of A Function

Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.

See similar textbooks

Related questions

Question

Assume that it costs a company approximately

C(x) = 700,000 + 250x + 0.0004x²

dollars to manufacture x game systems in an hour.

(a)

Find the marginal cost function, and use it to estimate how fast the cost is increasing when x = 60,000. Compare this with the exact cost of producing the 60,001st game system.

(b)

Find the average cost function

C(x)

and the average cost to produce the first 60,000 game systems.

(c)

Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 60,000 game systems.

Expert Solution

Step 1

Consider the cost of a company,

$C (x) = 700, 000 + 250 x + 0.0004 x^{2}$

To calculate the marginal cost of the function,

$\begin{matrix} C' (x) = \frac{d}{d x} (700, 000 + 250 x + 0.0004 x^{2}) \\ = \frac{d}{d x} 700, 000 + 250 \frac{d}{d x} x + 0.0004 \frac{d}{d x} x^{2} \\ = 0 + 250 \cdot (1) + 0.0004 (2 x) \\ C' (x) = 250 + 0.0008 x \end{matrix}$

Hence the marginal cost of the given function is 250+0.0008x

Trending now

This is a popular solution!

Step by step

Solved in 5 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Area$

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.

Similar questions