How does one derive the modified tanh activation proposed by LeCun?

In "Efficient Backprop" (http://yann.lecun.com/exdb/publis/pdf/lecun-98b.pdf), LeCun and others propose a modified tanh activation function of the form:

$$f(x) = 1.7159 * tanh(\frac{2}{3}*x)$$

They argue that :

• It is easier to approximate with polynomials
• It is said that it fit the target that it's second derivative is maximal in 1

I tried to start with a function of the form : $$f(x) = a * tanh(b*x)$$ and derive the value of $$a$$ and $$b$$ to match the aforementionned properties.

Any idea of how those constants are derived ? Under what assumptions ? Does it match its expected properties by construction ?