# Thread: Find max and min for function

1. ## Find max and min for function

$\displaystyle f(x)=e^{x^2-2x}$ for 0<= x <=2
(dont know how to insert less than or equal to)

2. Originally Posted by Minino777
$\displaystyle f(x)=e^{x^2-2x}$ for 0<= x <=2

$\displaystyle \frac{df}{dx}=\left(e^{x^2-2x}\right)(2x-2)$. Set to 0 to find critical points. Also don't forget to check the boundaries, x=0 and x=2.

Originally Posted by Minino777
(dont know how to insert less than or equal to)
In LaTeX, use \le (or \leq)

3. ## critical points

I only get one critical point x=1 within the boundaries, right?

4. Originally Posted by Minino777
I only get one critical point x=1 within the boundaries, right?
Yup, and that is also the only critical point within the domain of the function (all reals).

5. Originally Posted by Minino777
I only get one critical point x=1 within the boundaries, right?
Yes, but you should also look at the endpoints of the interval as well. This gives you 3 points to look at.

To find the minimum and maximum, evaluate the function at all 3 of those points and see which is the smallest and which is the largest.

6. Originally Posted by drumist
Yes, but you should also look at the endpoints of the interval as well. This gives you 3 points to look at.

To find the minimum and maximum, evaluate the function at all 3 of those points and see which is the smallest and which is the largest.