Maxima and minima of function

In summary, The conversation discusses finding the value of the first derivative of a function involving the variable r. The attempt at solving the problem involves using the chain rule and differentiating by parts. There is also a discussion about the notation exp(-r) meaning e^-r. The conversation ends with the person feeling more confident in their understanding and thanking the other person for their help.
  • #1
justin335
3
0

Homework Statement


Consider the following function of the variable r, r>/=0
y(r)=(r^(2)-5.50r)exp(-r)
Find the value of the first derivative dy/dr at r=5.50

Homework Equations


How do I solve this? I know its a simple derivative equation, but I can't seem to get it. I tried finding the derivative and then plugging in r=5.50 but MasteringPhysics says it incorrect.
Also, does exp(-r) mean to the -r power? I've never seen it written like that.


The Attempt at a Solution


Assuming exp(-r) means to the negative r power...
I tried using the chain rule;
y(r)=(r^(2)-5.50r)exp(-r)
dy/dr=-r(r^(2)-5.50r)^(-r-1)*(2r-5.50)
plugging in r=5.50, I get a 0, making the solution 0, which is obviously wrong...
I think its my poor calc skills, any help would be great, thanks!
 
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  • #2
exp(-r) is a representation of ##e^{-r}##.

So, your function is ##y(r) = (r^2-5.50r)e^{-r}##
 
  • #3
TSny said:
exp(-r) is a representation of ##e^{-r}##.

So, your function is ##y(r) = (r^2-5.50r)e^{-r}##

Thanks, would the derivative be e^-r(2r^3-16.5r^2+30.35r)? Thats what I got, and after subbing in r=5.5 again, I still get the answer wrong...
 
  • #4
justin335 said:
Thanks, would the derivative be e^-r(2r^3-16.5r^2+30.35r)? Thats what I got, and after subbing in r=5.5 again, I still get the answer wrong...

What's the derivative of ex with respect to x?

What's the derivative of e-x with respect to x?

Do you know how to differentiate by parts?
 
  • #5
Chestermiller said:
What's the derivative of ex with respect to x?

What's the derivative of e-x with respect to x?

Do you know how to differentiate by parts?

Oh ok, Ill have to reference my calc notes since I am pretty rusty. but I think I should get it now. Thanks for the help
 

1. What is a maxima and minima of a function?

A maxima and minima of a function are the highest and lowest values that the function reaches, respectively. They can also be referred to as the peak and valley points of the function.

2. How can I find the maxima and minima of a function?

To find the maxima and minima of a function, you can take the derivative of the function and set it equal to zero. Then, solve for the x-value(s) that make the derivative equal to zero. These x-values will correspond to the maxima and minima of the function.

3. What is the difference between local and global maxima/minima?

A local maxima/minima is the highest/lowest point within a specific interval of the function, while a global maxima/minima is the highest/lowest point of the entire function. A global maxima/minima can also be referred to as an absolute maxima/minima.

4. Can a function have multiple maxima or minima?

Yes, a function can have multiple maxima and minima. This can happen when the function has multiple peaks and valleys within a given interval or if the function is oscillating between positive and negative values.

5. How do maxima and minima relate to optimization problems?

Maxima and minima are important in optimization problems because they represent the optimal values that a function can reach. In optimization, we are trying to find the highest or lowest value of a function, which corresponds to the maxima or minima, respectively.

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