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midsol4 - 4(20 points(3 Define a convex function(on a...

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Unformatted text preview: 4. (20 points) (3) Define a convex function (on a convex set S). _ (b) Use the definition in part (a) to show that L(m) = 23; + 1 is a convex function (on the real line). . _ (c) Given that f (3:) is a convex function (on a convex set S), for what values of the real number a is the function h(m) = a f (I) also a convex function? ‘Show that inactive“: Mil as“; § ’ y_ mic—WM?) saucer) + (#4)}?ng (8%“) Lfio<2<fl+ZI—o<)7)k: g(p(x+(,PK)oy)+/ \ KLOGMF (P00h7) : ”WNW/M (”(9”ng ~2ng +d+(z»x)aa+‘/-°¢ , ‘ ”3 1(0<>G+(/~oz)j7+ l 21(4X+(/q<)7) MAT“? in»; aEIoZXA'U'd/ig) '5 09% +10“) ’87? {fl K20 aECMX+CF°W7I g 4(xfi0c)+(/‘°()78(7)) { :xa‘fitk) +(1’V\)¢Wfl‘7} , MyfiLUJggjé «(Am +U’QM‘77 51> CUM/30 , 0L Edi—t; 6x<0 (71% A MMMCPWW >°J~OG>+CP09 ‘7) ngfcwvax ...
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