Question

state and prove the necessary conditions for the existence of maximum value and minimum value?

Answer 1

$\text{It is said that function has at point c maximum } \\ \text{(or minimum) if there exist such number δ>0} \\ \text{ that for all x ∈ (c − δ, c + δ) we have that f(x) ≤ f(c) (or f(x) ≥ f(c)).}$