Show how to prove a function is convex. How to prove concave and convex must be linear function? How to prove that the cubic-bezier is second-order continuous? Prove the following by using Fundamental Theorem of Algebra. Does this use Rolle's theorem? How would one prove this?
How to prove if a polytope is bounded? How do you proof a function is convex? Prove by a mathematical indication that for all n greater than equal to 2, square root{n} less than Summation_{i=1}^{n} 1/square root{i}. How to prove if a function is convex?
Proposition 1 Any half-space is a convex set. Proof: Trivial. ◻ Proposition 2 Let X be a n.v.s. f∈X∗ such that f(X)=R . For any α∈R , the hyperplane H={f(x)=α} is closed iff f is continuous. Proof: X∖H open iff H is closed. Suppose f is continuous and...
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Answer to: If a function f :[a,b] \rightarrow \Re is bounded and has at most finitely many discontinuities on [a,b] , prove that f \in...
The function is continuous over its domain but it is not differentiable at {eq}x=0 {/eq} where it forms a corner (the point where the function's slope presents a finite jump).Answer and Explanation: Let us consider the expression, {eq}|ab|=|a||b| {/eq}. Let us call {eq}|...
Explain how to prove that the quantile of Gaussian distribution is convex. Quantile Function: Letpbe the proportion andF(.)be the CDF ofX, which follows the normal distribution. Then, the quantile function is defined as follows: Q(p)=F−1(p)=ϕ−1(p) ...