How can derivatives be used for optimization problems in calculus?

Derivatives are crucial in solving optimization problems in calculus. By finding the critical points of a function using the first derivative test and determining whether they are maxima or minima using the second derivative test, we can identify the optimal values of a function. These concepts are extensively used in real-world scenarios such as finding the maximum area or minimum cost of a structure. By understanding how derivatives relate to optimization, students can apply calculus to solve practical problems efficiently.