Maximum Value of a Function Calculation Using Symmetry
Explore how to find the maximum value of a function by leveraging symmetry principles. Learn the step-by-step process of determining the maximum value through calculations based on the provided parameters and equations from Perkins & Perkins Book.
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Find f(2) Based on Perkins & Perkins Book 1 Page 39 Ex 3.1 Q10
Find ?(2) The maximum value of the function ? ? = ??2+ ?? + ?is 10 Given that ? 3 = ? 1 = 2 , find? 2 . ? 3 = 9? + 3? + ? = 2 ? 1 = ? ? + ? = 2 From symmetry, the maximum must occur at ? = 1 (mid-way between ? = 1 and ? = 3) ? 1 = ? + ? + ? = 10 Solving the above equations gives: ? = 2 , ? = 4 , ? = 8 So ? 2 = 2 22+ 4 2 + 8 = 8
Note to Teacher Where the input parameters are: ? 2 = 8 ? 2 = 7 even, then odd, then There are eight of each type. You can create your own knowing the following: If the max/min value is ? and ? 3 = ? 1 = ? Then ? 2 =?+3? 4 and ? = ? ? 4 ? ? 2 ?+3? 4 , ? = , ? =
The maximum value of the function ? ? = ???+ ?? + ? is ?? The minimum value of the function ? ? = ???+ ?? + ? is ? Given that ? ? = ? ? = ?, find ? ? . Given that ? ? = ? ? = ??, find ? ? . Find?(?) Find?(?) SIC_37 SIC_37
The minimum value of the function ? ? = ???+ ?? + ? is ? The minimum value of the function ? ? = ???+ ?? + ? is ? Given that ? ? = ? ? = ??, find ? ? . Given that ? ? = ? ? = ??, find ? ? . Find?(?) Find?(?) SIC_37 SIC_37
The maximum value of the function ? ? = ???+ ?? + ? is ?? The maximum value of the function ? ? = ???+ ?? + ? is ?? Given that ? ? = ? ? = ?, find ? ? . Given that ? ? = ? ? = ??, find ? ? . Find?(?) Find?(?) SIC_37 SIC_37
The minimum value of the function ? ? = ???+ ?? + ? is ? The minimum value of the function ? ? = ???+ ?? + ? is ? Given that ? ? = ? ? = ??, find ? ? . Given that ? ? = ? ? = ??, find ? ? . Find?(?) Find?(?) SIC_37 SIC_37
The maximum value of the function ? ? = ???+ ?? + ? is ?? The minimum value of the function ? ? = ???+ ?? + ? is ?? Given that ? ? = ? ? = ??, find ? ? . Given that ? ? = ? ? = ??,find ? ? . Find?(?) Find?(?) SIC_37 SIC_37
The maximum value of the function ? ? = ???+ ?? + ? is ?? The maximum value of the function ? ? = ???+ ?? + ? is ? find ? ? . Given that ? ? = ? ? = ?, find ? ? . Find?(?) Find?(?) Given that ? ? = ? ? = ?, SIC_37 SIC_37
The minimum value of the function ? ? = ???+ ?? + ? is ? The minimum value of the function ? ? = ???+ ?? + ? is ? Given that ? ? = ? ? = ??, find ? ? . Given that ? ? = ? ? = ??,find ? ? . Find?(?) Find?(?) SIC_37 SIC_37
The minimum value of the function ? ? = ???+ ?? + ? is ? The minimum value of the function ? ? = ???+ ?? + ? is ? Given that ? ? = ? ? = ??, find ? ? . Given that ? ? = ? ? = ??, find ? ? . Find?(?) Find?(?) SIC_37 SIC_37
