To determine To calculate: The cost function, C ( x ) . Explanation Given: The marginal cost function is C ′ ( x ) = 2 x 3 + 6 x − 5 and fixed cost is C ( 0 ) = $ 800 . Formula used: The family of all anti-derivatives of the function f is denoted by ∫ f ( x ) d x . If F ′ ( x ) = f ( x ) , then ∫ f ( x ) d x = F ( x ) + C , for any real number C . Power rule of anti-derivatives is defined as: For any real number n ≠ − 1 , ∫ x n d x = 1 n + 1 x n + 1 + C Let f ( x ) and g ( x ) be functions that have anti-derivatives and let k be any real number. Constant Multiple Rule is: ∫ k f ( x ) d x = k ∫ f ( x ) d x Sum or difference rule is: ∫ [ f ( x ) ± g ( x ) ] d x = ∫ f ( x ) d x ± ∫ g ( x ) d x Calculation: Since C ′ ( x ) gives the rate of change of ‘ x ’. The cost function, C( x ) is calculated as: C ( x ) = ∫ C ′ ( x ) d x = ∫ ( 2 x 3 + 6 x − 5 ) d x Integrate using sum or difference rule to get: C ( x ) = ∫ ( 2 x 3 + 6 x − 5 ) d x

MATH W/APPLICAT.W/NOTES GDE +ACCESS CODE

11th Edition

ISBN: 9781323751671

Author: Lial

Publisher: PEARSON C

See similar textbooks

Concept explainers

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

Videos

Question

Chapter 13.1, Problem 8CP

To determine

To calculate: The cost function, C(x).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.1, Problem 7CP

Chapter 13.1, Problem 9CP

Students have asked these similar questions

Task number: A1.1, A1.7 Topic: Celestial Navigation, Compass - Magnetic and Gyro Activ Determine compass error (magnetic and gyro) using azimuth choosing a suitable celestial body (Sun/ Stars/ Planets/ Moon). Apply variation to find the deviation of the magnetic compass. Minimum number of times that activity should be recorded: 6 (2 each phase) Sample calculation (Azimuth- Planets): On 06th May 2006 at 22h20m 10s UTC, a vessel in position 48°00'N 050°00'E observed Mars bearing 327° by compass. Find the compass error. If variation was 4.0° East, calculate the deviation. GHA Mars (06d 22h): Increment (20m 10s): 089° 55.7' 005° 02.5' v (0.9): (+) 00.3' GHA Mars: 094° 58.5' Longitude (E): (+) 050° 00.0' (plus- since longitude is easterly) LHA Mars: 144° 58.5' Declination (06d 22h): d (0.2): N 024° 18.6' (-) 00.1' Declination Mars: N 024° 18.5' P=144° 58.5' (If LHA<180°, P=LHA) A Tan Latitude/ Tan P A Tan 48° 00' Tan 144° 58.5' A = 1.584646985 N (A is named opposite to latitude, except when…

Activ Determine compass error using amplitude (Sun). Minimum number of times that activity should be performed: 3 (1 each phase) Sample calculation (Amplitude- Sun): On 07th May 2006 at Sunset, a vessel in position 10°00'N 010°00'W observed the Sun bearing 288° by compass. Find the compass error. LMT Sunset: LIT: (+) 00d 07d 18h 00h 13m 40m UTC Sunset: 07d 18h 53m (added- since longitude is westerly) Declination (07d 18h): N 016° 55.5' d (0.7): (+) 00.6' Declination Sun: N 016° 56.1' Sin Amplitude = Sin Declination/Cos Latitude = Sin 016°56.1'/ Cos 10°00' = 0.295780189 Amplitude=W17.2N (The prefix of amplitude is named easterly if body is rising, and westerly if body is setting. The suffix is named same as declination) True Bearing=287.2° Compass Bearing= 288.0° Compass Error = 0.8° West

Chapter 13 Solutions

MATH W/APPLICAT.W/NOTES GDE +ACCESS CODE

Ch. 13.1 - Checkpoint 1 Find an antiderivative for each of...Ch. 13.1 - Checkpoint 2 Find each of the...Ch. 13.1 - Prob. 3CP Ch. 13.1 - Prob. 4CP Ch. 13.1 - Prob. 5CP Ch. 13.1 - Prob. 6CP Ch. 13.1 - Prob. 7CP Ch. 13.1 - Checkpoint 8 The marginal cost at a level of...Ch. 13.1 - 1. What must be true of F(x) and G(x) if both are...Ch. 13.1 - 2. How is the antiderivative of a function related...

Knowledge Booster

Learn more about

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