[CALCULUS—OPTIMIZATION] For positive constants A and B, the force between two atoms in a molecule is given by f(r) where r 0 is the distance between the molecules. What value of r minimizes the force between the atoms?

Question

[CALCULUS—OPTIMIZATION] For positive constants A and B, the force between two atoms in a molecule is given by f(r) where r > 0 is the distance between the molecules. What value of r minimizes the force between the atoms?

stamp · Answer

$$f(r)=-\frac{A}{r^2}+\frac{B}{r^3}$$

anonymous · Answer

Hello stamp

u just need to take the derivative of f(r) and set it equal to zero and solve it for r

stamp · Answer

That does not work.

anonymous · Answer

why? can u show me ur work ?

stamp · Answer

$$f'(r)=\frac{2A}{r^3}-\frac{3B}{r^4}$$

anonymous · Answer

quite right and what about solving $$f'(r)=0$$?

stamp · Answer

2Ar - 3B = 0

anonymous · Answer

and it gives$$r=\frac{3B}{2A}$$

anonymous · Answer

ok :)