The Question Reads As Follows:Decide If It Is Poss

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The question reads as follows: Decide if it is possible for a function to have an absolute maximumbut no absolute minima on the interval [-1,1]. Explain yourreasoning if you believe the answer is no, give the formula of sucha function if you believe the answer is yes. My initial guess was -(x2), but are the end pointsconsidered abs. minima if there's two of them?

 

Answer No.1

Anonymous

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The absolute minimum doesn't have to be unique, so your guess won'thelp much Consider the function f(x) = -1 / x^2 It diverges to negative infinity when approaching x = 0 from bothsides. This means there exists no x for which any y can be chosen so f(x)<= f(y) If you believe you did find such an x, feel free to take y = x /2 This function does have a maximum in the interval, namely at theendpoints

Answer No.2

Anonymous

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So pretty much what you're saying is that since the intervals areclosed, there will always have to be an absolute max and min onthat interval?

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