Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Let $C(x)=a x^{2}+b x+d$ represent the cost of producing $x$ items. Find the error if $C^{\prime}(x)$ is used for the marginal cost of the xth item.

$a$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 7

Marginal Functions and Rates of Change

Derivatives

Baylor University

University of Nottingham

Boston College

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

01:21

For the cost function C(x)…

01:12

01:18

Let $R(x)$ be the revenue …

02:55

If the cost of manufacturi…

01:09

Suppose the cost of produc…

03:04

00:29

Marginal Average Cost Supp…

because I have a cost function represented represented by mx plus B or X. Units, M and B are constants. So let's look at the cost of producing the 1000 and first item. So the cost will be M times 1000 and one plus B. So it's really just 1000 and one M plus B. What's the marginal cost here? Marginal implies rate of change of the costs. The rate of change, I'm looking at the first derivative of the first derivative of Mx is just um Derivative of BA zero. The marginal cost of the 1001st item just replaced. Um I am with nothing acts with nothing. So it's just um So what's going on here? Which is greater. So my original cost is actually going to be always greater than, yeah, my original is always greater than my marginal here because my marginal is just m of my 1001st cost. Whereas with my original costs I'm multiplying 1000 and one M plus B to each term.

View More Answers From This Book

Find Another Textbook

Numerade Educator

07:47

A small bottling company finds that it costs $6,000$ to prepare 10,000 six p…

06:52

Classify all critical points.$s(t)=2 t^{3}-9 t^{2}-60 t+5$

03:44

Use the second derivative test to classify the critical points.$$f(x)=(x…

03:27

$1 / t+1 / s=1 .$ Find $(a) d s / d r ;$ (b) $d t / d s,$ (c) Show that $(d …

02:01

Locate all critical points.$$f(x)=\left(x^{2}-9\right)^{2 / 3}$$

01:20

Use your calculator to compute the expression given.$$7^{-3.25}$$

02:29

If $y=x^{3}-3 x,$ determine $d y / d t$ when $x=2$ and $d x / d t=3$.

01:10

Find two numbers whose sum is 100 such that their product is as large as pos…

01:13

Find the average rate of change of $y$ with respect to $x$ on the given inte…

05:31

A rubber ball (a sphere) is expanding in such a way that its radius increase…