Traditional optimization is critical, using differential calculus to find the optimal value for unconstrained and constrained objective functions. Use differential calculus-based methods to achieve an optimum resolution of requests involving constant and differential tasks and adequate circumstances for finding an optimal reaction for emotional and restrained, single and multi-variable optimization problems with equivalence and in equivalence restraints. Make a distinction between local, global, and extreme inflection points. The purpose is to use the direct substitution method, Language multipliers method, and Kuhn-Tucker method have also been discussed to realize the optimal quantity of an empirical act with equality and inequality constraints. The findings are traditional optimization approaches achieve an optimal result of specific difficulties that involve continuous and differentiable functions. These procedures are logical, along with getting into the advantage of differential calculus to find maxima and minima points for a constrained single and multiple variable continuous function .The originality of my paper is using various methods for comparing Lagrange method, Kuhn-Tucker condition.