# Maxima and minima of function

1. Oct 22, 2012

### justin335

1. The problem statement, all variables and given/known data
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

2. Relevant 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.

3. 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!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Oct 22, 2012

### TSny

exp(-r) is a representation of $e^{-r}$.

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

3. Oct 22, 2012

### justin335

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. Oct 22, 2012

### Staff: Mentor

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. Oct 22, 2012

### justin335

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