Finding extremum in a polynomial function

A function given by $f(x)=\frac{(ax^2+2bx+c)}{(Ax^2+2Bx+C)}$ has points of extrema at $x=1$ and $x=-1$, such that $f(1)=2, f(-1)=3$ and $f(0)=2.5$. Then

1. Which of the following is true?
   • (A) $a= -2.5A$
   • (B) $a= 2.5A$
   • (C) $A= -2.5A$
   • (D) none of these
2. Which of the following is true?
   • (A) $b=B$
   • (B) $A=B$
   • (C) $c=C$
   • (D) $A=C$
3. What is the function? (in terms of $P/Q$, where $P$ and $Q$ are quadratic polynomials)

1 Answer

Hint: From $f(0)=2.5$, you get $c = 2.5C$. Similarly make equations using $f(1)=2,f(-1)=3, f^1(1)=0, f^1(-1)=0$