Calc
posted by Anonymous .
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 yaxis (meaning it has no odd powers of x), and which has a yintercept of 0, and global maxima at (4,512) and (−4,512).

p has maxima at 4,4 and is 3rd degree, so
p'(x) = ax(x^216)
= 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