Posted by Dana on Sunday, April 7, 2013 at 9:20pm.
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 10, and global maxima at (3,253) and (−3,253).

Calculus  Reiny, Sunday, April 7, 2013 at 10:46pm
let the function be
y = ax^4 + bx^2 + c
since (0,10) is on it > c = 10
dy/dx = 4ax^3 + 2bx
at (3,253), dy/dx = 0
4a(27) + 2b(3) = 0
108a + 6b = 018a + b = 0
b = 18a
at (3, 253) , dy/dx = 0
4a(27) + 2b(3) = 0 , this gives the same result, so nothing new here
but (3,253) lies on the actual curve
253 = 81a + 9b
sub in b = 18a
253 = 81a + 9(18a)
253 = 81a
a = 253/81
then b = 18(253/81) = 506/9
so y = (253/81)x^4 + (506/9)x^2 + 10
check:
dy/dx = 1012/81x^3 + 1012x = 0 for a max/min
divide by 1012
x^3/81  x = 0
times 81
x^3  81x = 0
x(x^2  9) = 0
x = 0 , or x = ±3
if x = 3 or 2
y = (253/81)(81) + (506/9)(9)
= 253 + 506 =253 YEAHHH
(weird coefficients)
Answer This Question
Related Questions
 Calc  Im not getting these answers at all, please help. Find a formula for the ...
 calculus  Find a formula for the fourth degree polynomial p(x) whose graph is ...
 calculus  fourth degree polynomial p(x) whose graph is symmetric about the y...
 Calculus  Find the equation of a quartic polynomial whose graph is symmetric ...
 PreCalculuscheck answers  The graph of the equation y=x^3x is symmetric with...
 College Algebra  1.The graph of y =  1/2 x  5  3 can be obtained from the ...
 4th grade math  The drill team is selling cookies to raise money. It costs .78...
 Math  Fundamental Theorem  We can actually use the Zeros Theorem and the ...
 MATH TRIGONOMETRY  refer to the polynomial function f(x)= x(x1)(x+2) in ...
 Precalculus  1. The graph of the equation y = x2 – 3 is symmetric with respect...
More Related Questions