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Question

Let u(x) be a twice differenctiable function defined in $0 less or equal than x less or equal than 1 comma$ holds the relation $u to the power of ´ ´ end exponent left parenthesis x right parenthesis equals e to the power of x end exponent u left parenthesis x right parenthesis text in end text x element of left square bracket 01 right square bracket. text If end text 0 less than x subscript 0 end subscript less than 1 comma$ then

u(x) can’t have a positive local maximum at x₀
u(x) can’t have a negative local maximum at x₀
u(x) can’t have a positive local minimum at x₀
u(x) can’t have any local maximum or minima at x₀

The correct answer is: u(x) can’t have a positive local maximum at x₀

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