Definition: In the context of mathematics, a "saddlebacked" function is an important concept in functional analysis. It refers to a function that has both continuous and differentiable derivatives at its critical points (those points where the derivative is not defined). These critical points are called saddles or singularities. The term is often used in the context of differential equations, particularly those with variable coefficients. A saddlepoint of a differential equation is a point where the gradient of the function is zero and the second
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