Question

4. The cost ($) of making x units of a certain item is given by $C(x) = 225 + 50x - 5x^2 + 0.2x^3$. (a) Evaluate $C'(15)$, and use it to estimate the additional cost in making another two (2) units when the production level is $x = 15$ units. (b) The slope of a line from the origin to point $(x, C(x))$ on the graph is $\frac{C(x)}{x}$; the average cost per unit at production level x. It appears the average cost would be minimum (the line is tangent) at about $x = 15$. Find the derivative $\frac{d}{dx} \left( \frac{C(x)}{x} \right)$, and evaluate it at $x = 15$.

          4.
The cost ($) of making x units of a certain item is given by $C(x) = 225 + 50x - 5x^2 + 0.2x^3$.
(a) Evaluate $C'(15)$, and use it to estimate the additional cost in making another two (2) units when
the production level is $x = 15$ units.
(b) The slope of a line from the origin to point $(x, C(x))$ on the graph is $\frac{C(x)}{x}$; the average cost per
unit at production level x. It appears the average cost would be minimum (the line is tangent) at
about $x = 15$.
Find the derivative $\frac{d}{dx} \left( \frac{C(x)}{x} \right)$, and evaluate it at $x = 15$.

Show more…

4.
The cost () of making x units of a certain item is given byC(x) = 225 + 50x - 5x^2 + 0.2x^3.
(a) EvaluateC'(15), and use it to estimate the additional cost in making another two (2) units when
the production level isx = 15units.
(b) The slope of a line from the origin to point(x, C(x))on the graph is(C(x))/(x); the average cost per
unit at production level x. It appears the average cost would be minimum (the line is tangent) at
aboutx = 15.
Find the derivative(d)/(dx) ( (C(x))/(x) ), and evaluate it atx = 15.

Added by Michelle O.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Eleni Katirtzoglou

07/10/2022

Step 1

C(x) = 225 + 50x - 5x^2 + 0.2x^3, so C'(x) = 0 + 50 - 10x + 0.6x^2 = 50 - 10x + 0.6x^2. Show more…

Show all steps

lock

Thanks for your feedback!

The cost ($) of making x units of a certain item is given by C(x)=225+50 x-5x^(2)+0.2x^(3). (a) Evaluate C^(')(15), and use it to estimate the additional cost in making another two (2) units when the production level is x=15 units. [4] (b) The slope of a line from the origin to point (x,C(x)) on the graph is (C(x))/(x); the average cost per unit at production level x. It appears the average cost would be minimum (the line is tangent) at about x=15. [4] Find the derivative (d)/(dx)((C(x))/(x)), and evaluate it at x=15. 4. The cost ($) of making x units of a certain item is given by C(x)=225+50x-5x2+0.2x3 (a) Evaluate C'(15) , and use it to estimate the additional cost in making another two (2) units when the production level is x = 15 units 800 700 [4] 600 500 C(400 300 200 100 01 5 10 15 20 x (b)The slope of a line from the origin to point (x, C(x) on the graph is : x unit at production level x. It appears the average cost would be minimum (the line is tangent) at about x = 15. 800 700 d (C(x) 600 Find the derivative and evaluate it at x=15 500 dx x C400 300 200- 100 0 0 5 10 15 20 x [4]

Play audio

Feedback

Powered by NumerAI

Eleni Katirtzoglou and 62 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later