The first step is to carefully read and understand the problem, identifying the objective function (the quantity to be maximized or minimized) and any constraints.
Defining variables clearly helps translate the word problem into mathematical equations, making it easier to formulate the objective function and constraints accurately.
Constraints are limitations or restrictions given in the problem, often expressed as inequalities. Identify key phrases like at least, at most, or not exceeding to find them.
Differentiation is primarily used. Find the critical points by setting the first derivative of the objective function equal to zero, and use the second derivative test to determine if they are maxima or minima.
Check the endpoints of the interval defined by the constraints, as well as any critical points within the interval, to ensure youve found the absolute maximum or minimum value.
Always check if your solution satisfies all the constraints given in the problem. If it doesnt, re-evaluate your approach or look for errors in your calculations.