Let with such that and
a) Compute the second-order Taylor series for in
b) Prove that defines as an implicit function of infinite class, of around Does have an extrema at ? Spoiler:
a) Second-order Taylor series is so for we have but I don't know how to compute nor
b) This case is strange to me to apply the IFT, what are the steps?
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We have and , so you can compute .
I don't know how to apply well the implicit function theorem for part b), can you give me a hand?
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