- Q1b F X For 271 Exercise 4 14 1convexity Show That The Following Function Is Convex 1 For X 1 Vlog X Justify Y 1 (118.38 KiB) Viewed 21 times
second derivative and if it was positive it is convex if it is
negative it was concave. but I am unsure what has been done here.
sorry about the answer its not my handwriting. could someone
explain simply what has been done here thank you
Q1b) f(x) = for 271 Exercise 4.14 - 1Convexity. Show that the following function is convex: 1 for x 1 Vlog (x) Justify your deduction by stating clearly which of the rules below you use: Lel V logic -Y2 Ihan) for azo va f(x) -((x)) Then h is convex, h is non-decreasing, & is convex his convex, h is non-increasing. is concave for 271 f is convex if { = » Ig(n) = lg Concave First, lets show glon) 3 gin)= loga for 271 Let's calulate the second derivative of ging d g(n) = 4 da على 1 <0 to g(n) is concave g(x) da2² x² is convex Next, to find if h (2) = x -122 or concave for rezo, calulate the decond derivative making use g the power rule & L" = 2"-
derivative first ¢ v) = (*) -4** -3/2 Finally, kechis convex, ħ (n) is non-increasing and gas is concave. Hence, fon)= 1 Vegion is convex second decvative d² doza 2 572 dele (RM)= 4 (32)) = 4x3. 512 because h"(n) = x Convex for 270 hen) is for all 470. re Yra to E 250 I ñ (a) = 하 0 20 which is non-increasing,