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Im not getting these answers at all, please help.

Find a formula for the fourth degree polynomial p(x) whose graph is symmetric about the y-axis (meaning it has no odd powers of x), and which has a y-intercept of 0, and global maxima at (4,512) and (−4,512).

  • Calc -

    p has maxima at 4,-4 and is 3rd degree, so
    p'(x) = ax(x^2-16)
    = 4ax^3 - 64ax

    p(x) = a x^4 - 32ax^2
    = a (x^4 - 32x^2)
    p(4) = 512, so a = -2

    p(x) = -2x^4 + 64x^2

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