If f(x) is a monic quartic polynomial such that f(-1) = -1, f(2) = -4, f(3) = -9, and f(4) = -16, find f(1).
+118608
\(f(x)=x^4+bx^3+cx^2+d\qquad \\ find\;\;f(1)\\ f(1)=1+b+c+d\\~\\ \\f(-1)=1-b+c+d=-1\\ c+d=-2+b\\ so\\ f(1)=1+b+-2+b\\ f(1)=-1+2b\\ \)
From there i found expressions for f(2), f(3) and f(4) and solved simulatneously to find b
I'll let you try it from there.
LaTex:
f(x)=x^4+bx^3+cx^2+d\qquad \\
find\;\;f(1)\\
f(1)=1+b+c+d\\~\\
\\f(-1)=1-b+c+d=-1\\
c+d=-2+b\\
so\\
f(1)=1+b+-2+b\\
f(1)=-1+2b\\
