# Homework Help: Calculus - Minimizing functions

1. May 20, 2014

### cutesteph

1. The problem statement, all variables and given/known data
Maximize the function for x. exp(-y+x-1) for y >= x-1 and y=x+e where e is distributed exp(L)

3. The attempt at a solution

d/dx(ln(exp(-y+x-1)) = 0 => d/dx(-y+x-1) = 0 but if I take the derivative of this x goes away.

2. May 20, 2014

### LCKurtz

What does "maximize the function for x" mean? And what is L? And what does "e is distributed exp(L) mean?

3. May 20, 2014

### cutesteph

Basically I am finding the maximum likelihood estimator x which is equivalent to maximizing the function exp(-y+x-1) where y >= x-1 .

e is representing error and distributed exponentially with parameter L means that it follows a distribution L*exp(-L*x).

4. May 20, 2014

### LCKurtz

Well, we aren't mind readers here. How would we know that "e" in your problem isn't the base of natural logarithms? You should include relevant details in your statement of the problem. I will let others respond to your question, now that I know what the subject area is.

5. May 20, 2014

### Ray Vickson

Are you describing two separate problems? I read it as:
Problem (1) $$\max_x \exp(-y+x-1),\\ \text{subject to } x-1 \leq y$$
and
Problem (2) $\max_x x+e, \: e \sim \text{expl}(L)$

If so, you have approached problem (1) incorrectly, since you cannot just set the derivative to zero in a constrained problem.

As stated, problem (2) makes no sense, for at least two reasons: (i) the thing you are maximizing is a random variable, not a real-valued function; and (ii) if there is no constraint on $x$ your "maximum" will be at $x = +\infty$.