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26 January, 04:55

Find a cubic function, in the form f (x) = ax^3+bx^2+cx+d, that has a local maximum value of 4 at - 3 and a local minimum value of 0 at 2. f (x) = ax3 + bx2 + cx + d.

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  1. 26 January, 05:21
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    Wea re given with f (x) = ax^3+bx^2+cx+d

    taking the first derivative

    f′ (x) = 3ax2 + 2bx + c

    substituting the conditions to the original equation

    f (-3) = 4=> - 27a + 9b-3c+d

    f (2) = 0=>8a+4b+2c+d

    f′ (-3) = 0=>27a-6b + c

    f′ (2) = 0=>12a+4b+c

    solving through the 4x4 solver

    a = 8/125

    b=12/125

    c=-1.152

    d=1.408

    The equation is equal to 8/125 x^3 + 12/125 x^2 - 1.152 x + 1.408.
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