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Jan 30, 2023 · Name two examples where the cohesive force dominates over the adhesive force and vice versa. When in a glass graduated cylinder, water presents an upwardly concave meniscus.
- Contact Angles
The intercept at zero velocity gives the value of r. Siebold...
- Contact Angles
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) + +.
A function $f(x)$ is said to be concave if the two conditions below satisfied: (i) $dom f$ is convex. (ii) For all $x,y\in dom f$ and $\theta\in[0,1],$ $$f(\theta x+(1-\theta)y) \geq \theta f(x) + (1-\theta)f(y)$$ In fact, this implies that if a function is convcave then that's also quasi-concave but not necessarily the converse is true.
Nov 21, 2023 · The rate of change of a function's derivative is called concavity. This is also known as the concavity definition. Concavity is an important property of the second derivative of a...
Review your knowledge of concavity of functions and how we use differential calculus to analyze it.
- You have two functions f and g, where f''>0 and g''>0. If you take the second derivative of f+g, you get f''+g'', which is positive. So their sum i...
- In order for 𝑓(𝑥) to be concave up, in some interval, 𝑓 ''(𝑥) has to be greater than or equal to 0 (i.e. non-negative) for all 𝑥 in that inter...
- In general, no. Points where f"(x)= 0 are specifically called inflection points. But in the example provided, -2 is also a critical point (Observe...
- Product rule: d/dx[f(x)*g(x)] = f'(x)g(x) + f(x)g'(x) f(x) = (x-1)³ and g(x) = x
Nov 14, 2023 · A concave function (sometimes called ''concave down'') is a function for which any secant line (a line connecting two points on the function) lies below the function. A concave function...
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A function that has an increasing first derivative bends upwards and is known as a convex function. On the other hand, a function, that has a decreasing first derivative is known as a concave function and bends downwards. We also describe a concave function as a negative of a convex function.
