If f : R" →R is C' (R") is convex then f(7) > f(x) + Vf(x)"(j – x) Vĩ,jeR" | 1. Use Taylor's theorem to prove (*).

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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1. If f : R" → R is C' (R") is convex then
f(7) > f(x) + Vf(x)" (j – x) Vĩ,j € R" .(*)
1. Use Taylor's theorem to prove (*).
2. Give a graphical interpretation of (*).
3. Use (*) to show
(Vf(F) – Vf(x))"(ỹ – x) > 0
Transcribed Image Text:1. If f : R" → R is C' (R") is convex then f(7) > f(x) + Vf(x)" (j – x) Vĩ,j € R" .(*) 1. Use Taylor's theorem to prove (*). 2. Give a graphical interpretation of (*). 3. Use (*) to show (Vf(F) – Vf(x))"(ỹ – x) > 0
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