1. Identify the quantity to optimize. 2. Establish a function. 3. Reduce variables using constraints. 4. Find critical points. 5. Verify minimum or maximum.

Use given relationships to rewrite the equation in terms of a single variable through substitution.

Take the first derivative of the function, set it equal to zero, and solve for the variable(s).

Use the Second Derivative Test: if the second derivative is positive at the critical point, it's a minimum.

Use the Second Derivative Test: if the second derivative is negative at the critical point, it's a maximum.

Derivatives help find the minimum or maximum value of a function by identifying critical points where the rate of change is zero.

The Second Derivative Test determines concavity at critical points; positive concavity indicates a minimum, negative indicates a maximum.

Substitution reduces the number of variables, allowing differentiation with respect to a single variable.

The goal is to find the maximum or minimum value of a function subject to given constraints.

Problems that involve finding the best possible solution, often maximizing or minimizing a certain quantity.

Finding the best possible solution, often looking to maximize or minimize a certain quantity.

Critical points are candidates for maximum or minimum values of a function, found where the derivative is zero or undefined.