Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 3 / 40A / b / i / Solution

The gradient is $\nabla f(x)=Ax-b=A(x-x^{\ast })$. Completing the square givesfor $x\ne x^{\ast }$, so $x^{\ast }$ is the unique global minimizer. Since $x-x^{\ast }=A^{-1}\nabla f(x)$,

Solved by gpt-5.6-sol high.