Simple application of Derivitives problem

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In summary, a simple application of derivatives problem involves finding the rate of change of a quantity at a specific point and can be used to solve real-world problems such as motion, growth, and optimization. Examples include finding velocity, maximum or minimum values, and population growth. To solve, you must identify variables, use differentiation rules, and plug in values. In science, this is important for modeling and understanding physical phenomena and making predictions. Tips for solving include identifying variables, using correct rules, and practicing different types of problems.
  • #1
Leonidas
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Find two positive numbers that satisfy the given requirements.


The Product is 192 and the sum is a minimum.


I said that x*y=192 and y=192/x and that dy/dx= -192/x^2

I thought that we were supposed to set the derivitive equal to zero in order to find the local extrema... however -192/x^2 does not equal 0...right?

I'm dazed and confused... can someone please help?
 
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  • #2
You should have done

[tex] xy = 192 [/tex]

[tex] y = \frac{192}{x} [/tex]

[tex] x + y = (number) [/tex]

Minimize this:
[tex] x + \frac{192}{x} = (number) [/tex]
 
  • #3
oh.

...

1. That was really fast... thanks.

2. I should have seen that.

3. :smile:
 

1. What is a simple application of derivatives problem?

A simple application of derivatives problem involves finding the rate of change of a quantity at a specific point. This can be used to solve real-world problems involving motion, growth, and optimization.

2. What are some common examples of simple application of derivatives problems?

Some common examples include finding the velocity of a moving object, determining the maximum or minimum value of a function, and calculating the rate of change of a population over time.

3. How do you solve a simple application of derivatives problem?

To solve a simple application of derivatives problem, you first need to identify the relevant variables and their relationship. Then, you can use the rules of differentiation to find the derivative of the function. Finally, plug in the given values to find the rate of change at the specific point.

4. What is the importance of simple application of derivatives in science?

Simple application of derivatives is important in science because it allows us to model and understand the behavior of various physical phenomena. It also helps us to make predictions and optimize processes in fields such as physics, biology, economics, and engineering.

5. What are some tips for solving simple application of derivatives problems?

Some tips for solving simple application of derivatives problems include carefully identifying the variables and their relationship, using the correct differentiation rules, and checking your final answer for correctness. It is also helpful to practice and familiarize yourself with different types of problems.

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