%3Cp%20class%3D%22c2%22%3EFind%20the%20critical%20points%20of%20the%0Afunction%2
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%3Cp%20class%3D%22c2%22%3EFind%20the%20critical%20points%20of%20the%0Afunction%20%3Cimg%20src%3D%0A%22https%3A%2F%2Fcourses1.webwork.maa.org%3A8080%2Fwwtmp%2Fequations%2F31%2F164959043c13c7037ef1c80eb1afbf1.png%22%0Aalt%3D%22f(x%2Cy)%3Dx%5E%7B4%7D%2By%5E%7B4%7D-64xy%22%20class%3D%22c1%22%20%2F%3E%3C%2Fp%3E%0A%3Cp%20class%3D%22c2%22%3E%3Cbr%20%2F%3E%3C%2Fp%3E%0A%3Cp%20class%3D%22c2%22%3EAnswer%20%3A%26nbsp%3B%3C%2Fp%3E%0A%3Cp%20class%3D%22c2%22%3E%3Cbr%20%2F%3E%3C%2Fp%3E%0A%3Cp%20class%3D%22c2%22%3EStarting%20with%20the%20point%20with%20the%0Asmallest%26nbsp%3B%3Cimg%20src%3D%0A%22https%3A%2F%2Fcourses1.webwork.maa.org%3A8080%2Fwwtmp%2Fequations%2Ffe%2F7ca85459d2390dbf4a5dfdd0b8b8e91.png%22%0Aalign%3D%22absmiddle%22%20alt%3D%22x%22%20class%3D%22c3%22%20%2F%3E%26nbsp%3Bvalue%2C%20use%20the%20Second%0ADerivative%20Test%20to%20determine%20whether%20each%20critical%20point%0Ais%26nbsp%3B%3Cbr%20%2F%3E%3C%2Fp%3E%0A%3Cp%20class%3D%22c2%22%3E%3Cimg%20src%3D%0A%22https%3A%2F%2Fcourses1.webwork.maa.org%3A8080%2Fwwtmp%2Fequations%2F5f%2F9157dc3e13816798871e3e6eb777f71.png%22%0Aalt%3D%22P_1%22%20class%3D%22c4%22%20%2F%3E%26nbsp%3B%3Cbr%20%2F%3E%0A%3Cinput%20type%3D%22radio%22%20name%3D%22AnSwEr0002%22%20id%3D%22AnSwEr0002%22%20value%3D%22A%22%0Aclass%3D%22c5%22%20%2F%3E%3Cb%3E%26nbsp%3BA.%26nbsp%3B%3C%2Fb%3Ea%20local%20minimum%26nbsp%3B%3Cbr%20%2F%3E%0A%3Cinput%20type%3D%22radio%22%20name%3D%22AnSwEr0002%22%20id%3D%22AnSwEr0002%22%20value%3D%22B%22%0Aclass%3D%22c6%22%20%2F%3E%3Cb%3E%26nbsp%3BB.%26nbsp%3B%3C%2Fb%3Ea%20local%20maximum%26nbsp%3B%3Cbr%20%2F%3E%0A%3Cinput%20type%3D%22radio%22%20name%3D%22AnSwEr0002%22%20id%3D%22AnSwEr0002%22%20value%3D%22C%22%0Aclass%3D%22c6%22%20%2F%3E%3Cb%3E%26nbsp%3BC.%26nbsp%3B%3C%2Fb%3Ea%20saddle%20point%26nbsp%3B%3Cbr%20%2F%3E%0A%3Cinput%20type%3D%22radio%22%20name%3D%22AnSwEr0002%22%20id%3D%22AnSwEr0002%22%20value%3D%22D%22%0Aclass%3D%22c6%22%20%2F%3E%3Cb%3E%26nbsp%3BD.%26nbsp%3B%3C%2Fb%3Etest%20fails%3Cbr%20%2F%3E%0A%3Cimg%20src%3D%0A%22https%3A%2F%2Fcourses1.webwork.maa.org%3A8080%2Fwwtmp%2Fequations%2Fd0%2F93bbd9866413f71b670032abc68d321.png%22%0Aalt%3D%22P_2%22%20class%3D%22c7%22%20%2F%3E%26nbsp%3B%3Cbr%20%2F%3E%0A%3Cinput%20type%3D%22radio%22%20name%3D%22AnSwEr0003%22%20id%3D%22AnSwEr0003%22%20value%3D%22A%22%0Aclass%3D%22c5%22%20%2F%3E%3Cb%3E%26nbsp%3BA.%26nbsp%3B%3C%2Fb%3Ea%20local%20minimum%26nbsp%3B%3Cbr%20%2F%3E%0A%3Cinput%20type%3D%22radio%22%20name%3D%22AnSwEr0003%22%20id%3D%22AnSwEr0003%22%20value%3D%22B%22%0Aclass%3D%22c6%22%20%2F%3E%3Cb%3E%26nbsp%3BB.%26nbsp%3B%3C%2Fb%3Etest%20fails%26nbsp%3B%3Cbr%20%2F%3E%0A%3Cinput%20type%3D%22radio%22%20name%3D%22AnSwEr0003%22%20id%3D%22AnSwEr0003%22%20value%3D%22C%22%0Aclass%3D%22c6%22%20%2F%3E%3Cb%3E%26nbsp%3BC.%26nbsp%3B%3C%2Fb%3Ea%20local%20maximum%26nbsp%3B%3Cbr%20%2F%3E%0A%3Cinput%20type%3D%22radio%22%20name%3D%22AnSwEr0003%22%20id%3D%22AnSwEr0003%22%20value%3D%22D%22%0Aclass%3D%22c6%22%20%2F%3E%3Cb%3E%26nbsp%3BD.%26nbsp%3B%3C%2Fb%3Ea%20saddle%20point%3Cbr%20%2F%3E%0A%3Cimg%20src%3D%0A%22https%3A%2F%2Fcourses1.webwork.maa.org%3A8080%2Fwwtmp%2Fequations%2Fd6%2Faa9c4eed1af65f7502ab5afc9e4e741.png%22%0Aalt%3D%22P_3%22%20class%3D%22c7%22%20%2F%3E%26nbsp%3B%3Cbr%20%2F%3E%0A%3Cinput%20type%3D%22radio%22%20name%3D%22AnSwEr0004%22%20id%3D%22AnSwEr0004%22%20value%3D%22A%22%0Aclass%3D%22c5%22%20%2F%3E%3Cb%3E%26nbsp%3BA.%26nbsp%3B%3C%2Fb%3Ea%20saddle%20point%26nbsp%3B%3Cbr%20%2F%3E%0A%3Cinput%20type%3D%22radio%22%20name%3D%22AnSwEr0004%22%20id%3D%22AnSwEr0004%22%20value%3D%22B%22%0Aclass%3D%22c6%22%20%2F%3E%3Cb%3E%26nbsp%3BB.%26nbsp%3B%3C%2Fb%3Etest%20fails%26nbsp%3B%3Cbr%20%2F%3E%0A%3Cinput%20type%3D%22radio%22%20name%3D%22AnSwEr0004%22%20id%3D%22AnSwEr0004%22%20value%3D%22C%22%0Aclass%3D%22c6%22%20%2F%3E%3Cb%3E%26nbsp%3BC.%26nbsp%3B%3C%2Fb%3Ea%20local%20maximum%26nbsp%3B%3Cbr%20%2F%3E%0A%3Cinput%20type%3D%22radio%22%20name%3D%22AnSwEr0004%22%20id%3D%22AnSwEr0004%22%20value%3D%22D%22%0Aclass%3D%22c6%22%20%2F%3E%3Cb%3E%26nbsp%3BD.%26nbsp%3B%3C%2Fb%3Ea%20local%20minimum%3Cbr%20%2F%3E%3C%2Fp%3E%0AExplanation / Answer
If a nonlinear programming problem has no constraints, the objective
function being concave (convex) guarantees that a local maximum (minimum)
is a global maximum (minimum).
?? What is a concave (convex) function?
?? A function that is always
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