Maxima and Minima in Algebra

What the exams ask here

• min of x^2+y^2 given x+y
• min value of expression with constraint
• f(x) = ax^2 + bx + c through (-2, 0), g(x) = -2x through (a, b) -> min of f(x) + 9a + 1 (Indore 2021 Q20)
• a^2 + b^2 + c^2 = 9 -> range of ab + bc + ca
• a + b + c = 13 -> max of (a - 3)(b - 2)(c + 1)
• min of px + q/x for x > 0