Finding critical values of hard functions

In summary, the speaker has been working on a problem for 2 hours and is having trouble finding the correct critical values. They have found the derivative of an equation and are unsure what to do with certain terms. They are trying to find the smallest area for a square and triangle with a given perimeter.
  • #1
hannazahhh
1
0

Homework Statement


I've been working on this problem for about 2 hours now and I can not get the right critical values. Please help.

Homework Equations


I found the derivative of the equation is sqrt(3/2) x-3/8 (10-3 x) and I've checked this over many times so I am pretty confident in my answer.

The Attempt at a Solution

I am sure what to do with the √2 and the 8 on the bottom. I did it with disregarding them and I now that's wrong but it cam up with the closet answer. I got it to the point of x+9x=30/√3 I get lost after that and I am pretty sure my work before this point is wrong also.

Homework Statement



im just trying to find the smallest area a square and triangle with perimeter some of 10 can be.
 
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  • #2
hannazahhh said:

Homework Statement


I've been working on this problem for about 2 hours now and I can not get the right critical values. Please help.


Homework Equations


I found the derivative of the equation is sqrt(3/2) x-3/8 (10-3 x) and I've checked this over many times so I am pretty confident in my answer.


The Attempt at a Solution

I am sure what to do with the √2 and the 8 on the bottom. I did it with disregarding them and I now that's wrong but it cam up with the closet answer. I got it to the point of x+9x=30/√3 I get lost after that and I am pretty sure my work before this point is wrong also.

Homework Statement



im just trying to find the smallest area a square and triangle with perimeter some of 10 can be.

I don't see an equation anywhere; an equation must have an '=' sign in it. Do you mean that you want to solve
[tex] \sqrt\frac{3}{2}\: x - \frac{3}{8} (10 - 3x) = 0?[/tex]
If so, that is just elementary algebra.
 

FAQ: Finding critical values of hard functions

What are critical values of hard functions?

Critical values of hard functions refer to the points on a graph where the derivative is equal to 0 or does not exist. These points are important because they can indicate the maximum or minimum value of a function, as well as points of inflection.

Why is it important to find critical values of hard functions?

Finding critical values allows us to understand the behavior of a function and make predictions about its maximum and minimum values. This information is useful in many applications, including optimization problems in engineering and economics.

How do you find critical values of hard functions?

To find critical values, we first take the derivative of the function and set it equal to 0. Then, we solve for the variable to find the x-values of the critical points. In some cases, we may also need to check for points of discontinuity or vertical tangents, which can also be critical values.

What is the significance of critical values in calculus?

Critical values play a crucial role in calculus because they help us determine the behavior of a function and its important points. They are also used in the process of finding the maximum or minimum value of a function, which is a fundamental concept in optimization and related applications.

Can critical values be negative?

Yes, critical values can be negative. The sign of a critical value depends on the behavior of the function and its derivative at that point. For example, a critical point with a positive derivative may correspond to a local minimum, while a negative derivative may indicate a local maximum.

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