# Ride The Saddle

Calculus Level pending

Consider the following class $$C^2$$ function $$f: \mathbb{R}^2 \to \mathbb{R}$$: $f(x,y) = 4xy^2 - 2x^2y - x + 1$

The $$xy$$-coordinates of the saddle points of $$f$$ are $$(a, b)$$ and $$(a, -b)$$.

Evaluate $$\dfrac{1}{a+b}$$.

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