Least Value of the Quadratic Expression

Question

What is the least value of this expression? Please show me a way to determine it.

Answer 1

Hints:

• Take the partials of each variable and equate to $0$ and solve for the point.
• For example $f_x = 2x - 2 = 0 \rightarrow x = 1$.

Spoiler

Minimum = $1$ at the point $\left(1, \dfrac{3}{2}, 1\right)$.

Answer 2

Just complete the squares: $(x-1)^2+(2y-3)^2+3(z-1)^2+1$