Please help lol: need step by step tutorials for 4 questions on Exam

[monstergamesgaming@gmail.]

Can't stop beating my head to the wall with this... can someone explain me step by step totarial for these?

 

[stapel]

Can't stop beating my head to the wall with this... can someone explain me step by step totarial for these?

If you really need tutorials over all of the material necessary to start working on these exercises, then you probably need to consider in-person tutoring. It is simply not reasonably feasible within this environment to attempt the days (or, more probably, the weeks) of direct instruction that you have implicitly requested.

Exam

Please note that this is not a "cheetz" site. Nobody here is going to take your test for you. Sorry. ("Read Before Posting")

Task 1: Business: minimizing average cost. The total cost in dollars of producing $x$ units of a product is given by:

$\qquad C(x) = 100x + 100\sqrt{x\,} + \dfrac{\sqrt[3]{x^3\,}}{100}$

How many units should be produced to minimize the average cost?

Start with the algebra. If the total cost $C$ of producing $x$ units is given by the posted expression, then what expression stands for the average cost of producing one of those units? (Hint: Divide by $x$, which is the total number of units produced, to create an expression for the average cost $A(x)$.)

Then turn to the calculus. You have a function for which you are seeking a minimum, so take the first and second derivative, applying the Quotient Rule (or Product Rule) and Chain Rule. Find any critical points, and then determine which, if any, is on an interval of upward concavity.

Task 2: Business: minimizing inventory costs. Ironside Sports sells $1225$ tennis rackets per year. It costs $$2$ to store one racket for a year. To reorder, there is a fixed cost of $$1$, plus $$0.50$ for each tennis racket. How many times per year should Ironside order tennis rackets, and in what lot size, in order to minimize inventory costs?

First, note that you will be making the assumption that purchases of tennis rackets is consistent throughout the year, rather than peaking at or near the beginning of weather conducive to playing tennis outdoors. You are also assuming that each order will be of the same size.

Work with the algebra. You are asked how many orders they should make, so pick a variable for "the number of orders". (The variable $x$ is fine.) You know that they will be needing to order $1225$ rackets over the course of the year. Then what expression stands for "the number of rackets in each order"? (Hint: Divide.)

And so forth.

Task 3: For $y = f(x) = x^2 - 3x$, $x = 5$, and $\Delta x = 0.1$, find $\Delta y$ and $f'(x)\, \Delta x$.

This is a fairly simple definition-application exercise. What definition did you learn for $\Delta x$? Apply the Power Rule to find the derivative. And so forth.

Task 4: Investigate the function. $y = (2x + 5)\cdot e^{-2(x+2)}$.

Unfortunately, we can't see your textbook/class notes, so we cannot know what is intended by the instruction to "investigate the function". You'll need to provide us with that information.

When you reply, please include a clear listing of your thoughts and efforts on each question on this test, or, if you have no knowledge of how to begin, specifically request links to lessons from which you can begin to learn the background material. (In the case of the latter, kindly please include a listing of topics, such as those covered by the relevant chapters/sections of your textook, for which you need online instruction.)

Please be complete. Thank you!

 

[monstergamesgaming@gmail.]

So as i understand the first task goes somethink like this...

 

[Harry_the_cat]

Whoa! Let's simplify things a bit.

What is A(x)? Simplify it before you find A ' (x).