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R C x g ́A } K W u ܂ ܂ v Ŕ Ă R ̃C x g ƃR T g ł B s I@Concrete758 ̃c C g shop info X R N g C _ X g h ƕRestriction of a convex function to a line f Rn → R is convex if and only if the function g R → R, g(t) = f(xtv), domg = {t xtv ∈ domf} is convex (in t) for any x ∈ domf, v ∈ Rn can check convexity of f by checking convexity of functions of one variable
Functions Inverse And Composite Functions
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MATH 140B HW 1 SOLUTIONS Problem1(WR Ch 5 #6) Suppose (a) f is continuous for x ‚0, (b) f 0(x) exists for x ¨0, (c) f (0) ˘0, (d) f 0 is monotonically increasing, Put g(x) ˘ f (x) x (x ¨0)and prove that g is monotonically increasing Solution If we can prove that g0(x) ¨0 for x ¨0, then this will show that g is monotonically increasing (by Theorem 511a) By the quotient rule,C x g Ղ襎 T h ЌP Ȃǂ̊ A ݉c A ^ C B Ƃ f o T r X L / C x g E E ^ E ݉cCompute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history
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