Question

Let f(x) be a polynomial of degree four having extreme values at x=1 and x=2.

Answer 1

limx→0(x2+f(x)x2)=3, since , limit exits hence x2+f(x)=ax4+bx3+3x2

⇒ f(x)=ax4+bx3+2x2

⇒ f(x)=4ax3+3bx2+4x

also f(x)=0 at x=1,2

⇒ a=12,b=−2

⇒ f(x)=x42−2x3+2x2

⇒ f(x)=8−16+8=0