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Taking the second derivative actually tells us if the slope continually increases or decreases. When the second derivative is positive, the function is concave upward. When the second derivative is negative, the function is concave downward.
So, when is a function concave or convex? A function f is concave if the 2nd derivative f’’ is negative (f’’ < 0). Graphically, a concave function opens downward, and water poured onto the curve would roll off. A function f is convex if f’’ is positive (f’’ > 0).
Dec 21, 2020 · When the graph is concave up, the critical point represents a local minimum; when the graph is concave down, the critical point represents a local maximum. We have been learning how the first and second derivatives of a function relate information about the graph of that function.
Convex curves, or convex functions are curves that curve upwards. Graphically, if a curve is above the line segment connecting any two points on it, the curve is said to be convex. Conversely, concave functions curve downwards.
Aug 16, 2019 · Positive-definite then your function is strictly convex. Positive semi-definite then your function is convex. A matrix is positive definite when all the eigenvalues are positive and semi-definite if all the eigenvalues are positive or zero-valued.
Convex and Concave functions and inflection points. Convex and concave are words that we use to describe the shape or curvature of a curve. Recall from classifying stationary points (see Stationary Points page) that we can find the second derivative of a function by differentiating twice.
