Solution-Using the convex-combination condition of convex

Using the convex-combination condition of convex function

Reference no: EM131211369

1. Show that x² is a strictly convex function on R without using any knowledge of the differentiability of the function (that is, using the convex-combination condition of a convex function).

2. Prove that a concave function is quasiconcave. Is the opposite assertion true? That is, if a function is quasiconcave, is it concave? Justify your answer.

3. Show that f(x) = √x is a concave function.

4. Consider the quadratic form f : R²→R defined by

Find the critical points of this function on R² and discuss whether they are maxima, minima or saddle points.

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The given function is f(x)=x^2 To prove this, let’s consider a function g(x)=(ax)^2. Let the function be f(y) and let the convex set is defined by S Let a be a real number. Let x and y be points in the upper level set P_a such that x?P_a and y?P_a

Reference no: EM131211369

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Using the convex-combination condition of convex function

Reference no: EM131211369

Reference no: EM131211369

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