1. ## Optimization

"for positive constants A and B, the force between 2 atoms in a molecule is given by

f(r)=-(A/r^2)+(B/r^3)

where r > 0 is the distance between the atoms. What value of r minimizes the force between the atoms?"

I can't quite seem to get a grasp on this.

2. Originally Posted by Nitz456
"for positive constants A and B, the force between 2 atoms in a molecule is given by

f(r)=-(A/r^2)+(B/r^3)

where r > 0 is the distance between the atoms. What value of r minimizes the force between the atoms?"

I can't quite seem to get a grasp on this.
One of those "well-behaved" functions.

Proceede by taking the derivative and making it zero.

$f'(r)=2A/r^3-3B/r^4$
$0=2A/r^3-3B/r^4$
Multiply through by $r^4$
Thus,
$0=2Ar-3B$
Thus,
$r=3B/2A$, if $A\not = 0$

3. Thanks a million sir!