Download the App!
Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.
Question
Answered step-by-step
The cost function for a certain commodity is$ C(q) = 84 + 0.16q - 0.0006q^2 + 0.000003q^3 $(a) Find and interpret $ C'(100). $(b) Compare $ C'(100) $ with the cost of producing the 101st item.
Video Answer
Solved by verified expert
This problem has been solved!
Try Numerade free for 7 days
Like
Report
Official textbook answer
Video by Heather Zimmers
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
02:25
Clarissa Noh
Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 7
Rates of Change in the Natural and Social Sciences
Derivatives
Differentiation
Oregon State University
Baylor University
University of Michigan - Ann Arbor
University of Nottingham
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.
44:57
In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.
06:12
30. The cost function for …
03:10
34. The cost function for …
06:13
02:05
The cost function for prod…
03:17
The cost (in dollars) of p…
01:12
For the cost function C(x)…
05:34
The average cost per item …
02:55
If the cost of manufacturi…
here we have a cost function and were asked to find See Prime of 100. And what that is is what's called the marginal cost. And that would be the cost of producing the 101st item if you've already produced 100 items. So in order to find that we start by finding the derivative in general, see prime of Q and we would get 0.16 minus 0.12 q plus 0.0 Hopefully, we have the right number of zero's nine Q squared. Okay, so that then we're going to take 100 substituted into that equation. And this would be a great use of your calculator and you're going to get 0.13 0.13 So what does that mean? That is an estimate of the cost of the 101st item. Okay, so for part B were told to find the actual cost of the 101st item and the way to find the actual cost would be to find the cost for 101 items that would be the total for making 101 minus the cost for making 100 items and see what we get. And so we're going to use our calculator for this with the original equation equation. Put 101 in there and we get 97.13 and then we put 100 in there and we get 97. And when we subtract those noticed that we get 0.13 that was would be 13 cents. So our estimate of the cost of the 101st item was very, very correct. It was the same as far as we can tell.
View More Answers From This Book
Find Another Textbook
Find the value of the integral f(r) = sin" I :indf (#}f 2 2[
How is the derivative of differentiable function f(x,y,z) at a point Po in t…
00:50
[ 1dr x22322ln2Submit
02:12
A new cell phone is introduced into the market It is predicted that sales wi…
02:08
A table of values of a function f with continuous gradient is given. Find
03:25
Bil and Mary Ann went to the Viola bakery: Bill bought danishos and of past…
02:00
[6 points] Solvecos * = - 0.875 for x in [0, Zpi) angle: Procedure using…
02:45
1.(10 pts) Find the general solution forthe equationty
04:44
Let 0 arctan(3/4) and 0 arccos( -8/17). First, SKETCH these angles, I separa…
01:39
1) Let G be the graph of function f (x) to graph the following function: f(x…
