Question

QNo.4. Check the convexity for following function. 1 © O ∞

Answer 1

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R2 P Ri 2. line pa *> we know that, a Planer region. R is called convex if and only if for any pair of points P,9 in R, the line pa liep completely in R. convex Non-convex (or concave) clearly, from the definition, it is clear that it is not convex. Here the line completely lies outside the set. Also, we see that, for every pair of points inside the set, the line lies wholly on the set. This, it is convex. Here we see that for the two WA selp give, if we take p q as points, then ref Pd does not lie b wholly within the set. so, is not convex from the definition, it is clear that for every pair P. q, the So, it is convex. A D / b