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Cake day: June 13th, 2023

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  • no, you need to derivate the f(x) function twice because the last line asks for f"(x). you do that by taking down the exponent in front of each power of the polynomial and decreasing the power by one each time you derivate.

    So for the 13x³: derived once it becomes 3 times 13 x², which equals 39x². Derived a second time, it is 2 times 39x, so 78x.

    The 11x² becomes 2 times 11x, and then just 22 (times x power zero). the rest disappears after two derivatives.

    The x is given when finding the correct pattern that matches the missing symbol in the first part of the problem, being the dot, so 52. I explained how you find this in a comment somewhere up here :)



  • no the correct pattern is 52, using the following method:

    • for each column, superpose the outer diagonal lines of the first and second pattern, lines that appear in both symbols are suppressed in the third (bottom) pattern, lines that only appear in one of the two first patterns are kept.
    • for each column, superpose the clock hands of the first and second pattern, only keep the clock hands that appear in both symbols at the same position.

    The third column has the same diagonal lines in the first and second pattern, so they disappear. Those two symbols have different clock hands so they also disappear. So the only remaining element in the pattern is the central dot (52).