calculus
posted by jay .
fourth degree polynomial p(x) whose graph is symmetric about the yaxis, and which has a yintercept of 10, and global maxima at (1,13) and (1, 13).

If it is even, P(x)=ax^4+bx^2+c
P(0)=10 so c is 10
p'=5ax^3+2bx=0
x(5ax^2+2b)=0
maximum at x=+1
so 5ax^2=2b
or 5a=2b or a=5/2 b
but P(1)=13=(5/2 b)*1+ b(1)+10
or 3/2 b=10 b=20/3 and a=5/2 * 20/3=100/6
check P(1)=13
it checks. 
Why do we end up with f(x) instead of f(t) on the Second Fundamental Theorem of Calculus?

5x^2