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
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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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}|...
How to prove the sine is convex? Derivative: f′(x) limh→0f(x+h)−f(x)h. f″(x)>0 Answer and Explanation:1 We havef(x)=sinx Now differentiate the function with respect to the variable x, we get, f′(x)=cosx