# The total cost C(x) in Rupees, associated with the production of x units of an item is given by C(x)=0.005x3−0.02x2+30x+5000 . Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change

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## To find the marginal cost when 3 units are produced, we need to follow these steps:Step 1: Understand the given functionThe total cost function is given by:C(x)=0.005x3−0.02x2+30x+5000Step 2: Find the derivative of the cost functionThe marginal cost is defined as the derivative of the total cost function with respect to x. We will differentiate C(x):C′(x)=ddx(0.005x3)−ddx(0.02x2)+ddx(30x)+ddx(5000)Calculating each term:- The derivative of 0.005x3 is 0.015x2- The derivative of −0.02x2 is −0.04x- The derivative of 30x is 30- The derivative of the constant 5000 is 0So, we have:C′(x)=0.015x2−0.04x+30Step 3: Evaluate the derivative at x=3Now we need to find the marginal cost when x=3:C′(3)=0.015(32)−0.04(3)+30Calculating 32:32=9Now substituting:C′(3)=0.015(9)−0.04(3)+30Calculating each term:C′(3)=0.135−0.12+30Now, combining the terms:C′(3)=30.135−0.12=30.015Step 4: ConclusionThus, the marginal cost when 3 units are produced is:Marginal Cost=30.015 Rupees---

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Updated on:7/8/2024

### Knowledge Check

• Question 1 - Select One

## If the total cost of producing x units of a commodity is given by C(x)=13x2+x2−15x+300, then the marginal cost when x=5 is

ARs 25
BRs 20
CRs 30
DRs 50
• Question 2 - Select One

## If C(x)=3x2−2x+3, the marginal cost when x = 3 is

A24
B16
C11
Dnone of the above

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    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

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TYPE: <one of the following values>
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- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
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# The total cost C(x) in Rupees, associated with the production of x units of an item is given by C(x)=0.005x3−0.02x2+30x+5000 . Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change

Video Solution
Text Solution
Generated By DoubtnutGPT

## To find the marginal cost when 3 units are produced, we need to follow these steps:Step 1: Understand the given functionThe total cost function is given by:C(x)=0.005x3−0.02x2+30x+5000Step 2: Find the derivative of the cost functionThe marginal cost is defined as the derivative of the total cost function with respect to x. We will differentiate C(x):C′(x)=ddx(0.005x3)−ddx(0.02x2)+ddx(30x)+ddx(5000)Calculating each term:- The derivative of 0.005x3 is 0.015x2- The derivative of −0.02x2 is −0.04x- The derivative of 30x is 30- The derivative of the constant 5000 is 0So, we have:C′(x)=0.015x2−0.04x+30Step 3: Evaluate the derivative at x=3Now we need to find the marginal cost when x=3:C′(3)=0.015(32)−0.04(3)+30Calculating 32:32=9Now substituting:C′(3)=0.015(9)−0.04(3)+30Calculating each term:C′(3)=0.135−0.12+30Now, combining the terms:C′(3)=30.135−0.12=30.015Step 4: ConclusionThus, the marginal cost when 3 units are produced is:Marginal Cost=30.015 Rupees---

|
Updated on:7/8/2024

### Knowledge Check

• Question 1 - Select One

## If the total cost of producing x units of a commodity is given by C(x)=13x2+x2−15x+300, then the marginal cost when x=5 is

ARs 25
BRs 20
CRs 30
DRs 50
• Question 2 - Select One

## If C(x)=3x2−2x+3, the marginal cost when x = 3 is

A24
B16
C11
Dnone of the above

Doubtnut is No.1 Study App and Learning App with Instant Video Solutions for NCERT Class 6, Class 7, Class 8, Class 9, Class 10, Class 11 and Class 12, IIT JEE prep, NEET preparation and CBSE, UP Board, Bihar Board, Rajasthan Board, MP Board, Telangana Board etc
NCERT solutions for CBSE and other state boards is a key requirement for students. Doubtnut helps with homework, doubts and solutions to all the questions. It has helped students get under AIR 100 in NEET & IIT JEE. Get PDF and video solutions of IIT-JEE Mains & Advanced previous year papers, NEET previous year papers, NCERT books for classes 6 to 12, CBSE, Pathfinder Publications, RD Sharma, RS Aggarwal, Manohar Ray, Cengage books for boards and competitive exams.
Doubtnut is the perfect NEET and IIT JEE preparation App. Get solutions for NEET and IIT JEE previous years papers, along with chapter wise NEET MCQ solutions. Get all the study material in Hindi medium and English medium for IIT JEE and NEET preparation
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The text passage contains a mathematical question related to finding the marginal cost of producing a certain number of units, and it provides a detailed step-by-step solution to the problem.

TYPE: SINGLE_QUESTION_WITH_ANSWER