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For example, x ∗ is a strict global maximum point if for all x in X with x ≠ x ∗, we have f(x ∗) > f(x), and x ∗ is a strict local maximum point if there exists some ε > 0 such that, for all x in X within distance ε of x ∗ with x ≠ x ∗, we have f(x ∗) > f(x). Note that a point is a strict global maximum point if and only if ...
Photovoltaic solar cell I-V curves where a line intersects the knee of the curves where the maximum power transfer point is located. In mathematics , a knee of a curve (or elbow of a curve ) is a point where the curve visibly bends, specifically from high slope to low slope (flat or close to flat), or in the other direction.
A saddle point (in red) on the graph of z = x 2 − y 2 (hyperbolic paraboloid). In mathematics, a saddle point or minimax point [1] is a point on the surface of the graph of a function where the slopes (derivatives) in orthogonal directions are all zero (a critical point), but which is not a local extremum of the function. [2]
A turning point of a differentiable function is a point at which the derivative has an isolated zero and changes sign at the point. [2] A turning point may be either a relative maximum or a relative minimum (also known as local minimum and maximum). A turning point is thus a stationary point, but not all stationary points are turning points.
A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v are also shown.. The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them.
This curve will in general have different curvatures for different normal planes at p. The principal curvatures at p, denoted k 1 and k 2, are the maximum and minimum values of this curvature. Here the curvature of a curve is by definition the reciprocal of the radius of the osculating circle. The curvature is taken to be positive if the curve ...
For a smooth curve given by parametric equations, a point is an inflection point if its signed curvature changes from plus to minus or from minus to plus, i.e., changes sign. For a smooth curve which is a graph of a twice differentiable function, an inflection point is a point on the graph at which the second derivative has an isolated zero and ...
A critical point of such a curve, for the projection parallel to the y-axis (the map (x, y) → x), is a point of the curve where (,) = This means that the tangent of the curve is parallel to the y -axis, and that, at this point, g does not define an implicit function from x to y (see implicit function theorem ).