(5-17)   ①  We can find a turning point by differentiating the energy expression and finding a value where the derivative equals zero:

So, at the turning point, dE/d<r> = 0, and hence:

Multiplying both sides by <r>2 and rearranging then gives:

②  Substituting in the values given, we get:

③  Finding the second derivative:

Substituting in the numbers again we find, when <r> =  4.0 x 10-11 m, 

d2E/d<r>2  =   -7210 + 10740  =  +3530

The positive value of the second derivative shows that this is indeed a minimum in the energy function.