# Homework Help: Optimization - Finding Minimum Between (0,0) and e^x

1. Dec 29, 2008

### carlodelmundo

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

Find the minimum distance from the origin to the curve y = e^x.

2. Relevant equations

Distance Formula

3. The attempt at a solution

http://carlodm.com/calc/prob6.jpg [Broken]

5-6 bright Calculus kids in my high school grappled with this problem and we couldn't find an answer.

Can anyone verify my solution? To simplify calculations, I minimized the inner quantity (underneath the square root of the Distance Formula). I feel, though, that this may have changed the answer. Answers are so close that I may have made a mistake.

Last edited by a moderator: May 3, 2017
2. Dec 29, 2008

### tiny-tim

Hi carlodelmundo!
Looks good to me.

(and minimising the inner quantity x2 + e2x is the same as minimising √(x2 + e2x))

3. Dec 29, 2008

### carlodelmundo

okay! just checking. Thank you tiny-tim.

I thought that since the derivatives of √(x^2 + e^2x)) and x^2 + e^2x are different, there could have been a discrepancy in my answer.

4. Dec 29, 2008

### tiny-tim

nah … if f'(x)/2√(f(x)) = 0, then that's the same as f'(x) = 0 (unless f(x) can be infinite).