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Sep 12, 2024 · Concavity in a function refers to the shape of the graph resembling a 'U' or an upside-down 'U'. When a function is concave up, it looks like a smile, and when it is concave down, it looks like a frown.
Oct 23, 2023 · Describe the concept of concavity and how it relates to the graph of a function. Difficulty: Medium Discuss the significance of interval notation in determining the intervals on which a function is concave up.
Concavity. The graph of a differentiable function y = f (x) is. (1) Concave up on an open interval I if f' is increasing on I; (2) Concave down on an open interval I if f' is decreasing on I. Second Derivative Test. Suppose that f'' (x) exists for all x values in open-interval (a,b)
To focus on a near object – the lens becomes thicker, this allows the light rays to refract (bend) more strongly. To focus on a distant object – the lens is pulled thin, this allows the...
Learn about and revise lenses, images, magnification and absorption, refraction and transmission of light with GCSE Bitesize Physics.
Definition 1. A function f : S ⊂ Rn → R defined on a convex set S is concave if for any two points x1 x2 ∈ , S and for any λ ∈ [0, 1] we have: λx1 (1 − λ) x2 ≥ λf(x1) (1 − λ)f(x2) + +. is called strictly concave if for any two points x1 , x2 ∈ S and for any λ ∈ (0, 1) we have: λx1 (1 − λ) x2 > λf(x1) (1 − λ)f(x2) + +.
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