For positive a b the force between two atoms is a function

Question

Question: For positive A, B, the force between two atoms is a function of the distance, r, between them:

f(r) = (-A/r²) + ( B/r³)    r > 0

(a) What are the zeros and asymptotes of f?

(b) Find the coordinates of the critical points and inflection points of f.

(c) Graph f.

(d) Illustrating your answers with a sketch, describe the effect on the graph of f of:

(i) Increasing B, holding A fixed

(ii) Increasing A, holding B fixed