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).
+118703
f(x)=x4+bx3+cx2+dfindf(1)f(1)=1+b+c+d f(−1)=1−b+c+d=−1c+d=−2+bsof(1)=1+b+−2+bf(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\\
